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Modelling, Simulation & Optimization in a Data rich Environment

A window of opportunity to boost innovations in Europe

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Modelling, Simulation & Optimization (MSO) remain thecornerstone for the development of most products inthe fields of Industry, Health, Energy or even Finance.Although High Performance Computing, Data Analyticsand Artificial Intelligence offer new opportunities, theirimpact on innovation and the improvement of productsand services could remain partial without a massiveeffort on the axes of modelling, simulation andcomplex systems optimization. Major opportunities,in particular, the establishment of digital twins, rely on the connections at the interface between fields of expertise, domains, businesses and across thecomplete lifecycle of products & systems. At the sametime, methods have outpaced computational power in terms of capability over the past decades. Ourinitiative is guided by the certainty that a high levelapproach on Modelling, Simulation & Optimization,enriched by data analytics and intensive computing, is a considerable economic asset.

Our core group represents a vast network of firms atthe European scale, aggregated through the nationalcommunities into the EU-MATHS-IN organization.Beyond the size of the current network, we are proudof the presence aboard of major European Simulationfirms (SIEMENS, ESI), of a living network of SMEs, andmany firms grounding the performance of theirproducts on mathematical expertise. We have

definitely achieved successes by the construction ofvarious national networks, which connect SMEs withacademic expertise in order to deliver innovativeapproaches and eventually new businessopportunities. In France, it has been named as theMSO Network. We are convinced our action, whenreally taken to the European scale, will increase theconnection between competences, promoteinnovative ideas for SMEs as well as for Large Firms,offer business synergies at the interface betweennon-competing interests, and reinforce the scientificand technological European leadership. This is alsounderlined by recent studies predicting that DigitalTwins relying on technological leaps in Modelling,Simulation & Optimization will cover a novel marketup to 90 billion dollars by 2025.

The following pages detail the opportunity andwitness concrete applications in alignment with thecorporate strategies of the firms pertaining to the EU-MATHS-IN Industrial Core Team.

Several contacts are now established on the side of national research agencies and decision makingEuropean structures. We look forward to identifyingthe final structure of the initiative we advise in acollaborative state of mind, in order to achieve thestakes we envision.

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Introduction

Vision for the initiative On the one hand, the future development of industryand society exhibits strongly increasing complexityand at the same time ever-shorter innovation cycles.On the other hand, digitisation and the internet ofthings have led to an explosion of data andinformation. Without novel computational tools andparadigms we will not be able to manage thesechallenges. There is a clear need to strengthenEuropean competitive advantage in industrialinnovations and to start a new initiative to meet theassociated societal challenges ahead of us.For almost all domains of science and engineeringand in almost all industrial sectors, model basedapproaches are well established. A multitude ofcommercial and open source software for modelling,simulation and optimization (MSO) based onmathematical models is available. At the same timeincreasingly large amounts of process and productdata are available and strong artificial intelligence

solutions have been developed to exploit these. Allthis is fostered by computers becoming more andmore powerful.

These developments lead to the vision that in thenear future holistic approaches can be achieved thatcombine all these developments. A completeindustrial product or process in its whole life cycle canbe accompanied by a virtual representation, oftencalled digital twin that allows design optimization,process control, lifecycle management, predictivemaintenance, risk analysis and many other features1. Digital twins are so important to business today, thatthey were named one of Gartner’s Top 10 StrategicTechnology Trends for 20172. They are becoming abusiness imperative, covering the entire lifecycle of anasset or process and forming the foundation forconnected products and services. Companies that failto respond will be left behind.

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MSO for Digital Twins (DT)Novel Modelling, Simulation and Optimisation paradigms in a Data rich Environment(MSODE)

This document serves as a discussion paper on the technological challenges needed toimplement, in a systematic and structured way, digital twins in industry and society and makethese a business success. Many components to achieve this are in place, but there is missingcapability on the side of mathematical modelling, simulation and optimisation as a key enabler,especially in data rich environments.

To establish this vision or to even come close to it,several new developments that involve differentscientific communities have to take place and manyobstacles have to be removed. A core need are novelmathematical technologies, to describe, to structure,to integrate and to interpret across disciplines.Mathematics is the language of digital twins.

History3

NASA was the first to dabble with pairing technology –the precursor to today’s digital twin – as far back asthe early days of space exploration. How do youoperate, maintain, or repair systems when you aren’twithin physical proximity to them? That was thechallenge NASA’s research department had to facewhen developing systems that would travel beyondthe ability to see or monitor physically.

Michael Grieves at the University of Michigan firstwrote of the concept using the digital twinterminology in 20024. The digital twin serves as a

bridge between the physical and digital world. Thecomponents are connected to a cloud-based systemor a dedicated hardware that uses sensors to gatherdata about real-time status and working condition.This input is analysed against business and othercontextual data. Lessons are learned andopportunities are uncovered within the virtualenvironment that can be applied to the physicalworld.

Digital twins are powerful masterminds to driveinnovation and performance. It is predicted footnotethat companies who invest in digital twin technologywill see a 30 percent improvement in cycle times ofcritical processes.

State-of-the-art Although first successes are reported5 and manyclaims are made6, neither the classical MSOapproaches based on mathematical models and theirsoftware implementations, nor the constantlyimproving techniques for data analysis and machinelearning will be enough to achieve this visionarygoal7,8. Even the rapid improvements in moderncomputing hardware and especiallyalgorithms/software are not sufficient to achieve this.Currently, due to the high manual human effort7, onlymajor companies with large R&D departments canafford to build digital twins, but it would be desirablethat companies on all scales can profit from thedevelopment. New generations of mathematicalparadigms are required to convey today’s highlyfragmented approaches in the various disciplines.

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Figure 1. Concept of a digital twin (picture taken from the reference in footnote 4)

Technology Challenges Currently, models, methods, as well as softwareimplementations and data sets are of highly differentfidelity requiring many manual interactions. The figureabove summarizes these interactions in a schematicway (including the interactions with existing initiatives).To meet the future challenges, it is necessary todevelop novel MSO paradigms allowing a systematicMSO based approach to build highly automatedmodularized networks of model hierarchies (fromvery high fidelity physics based models to very coarse,surrogate, or even purely data based models), andthat can deal with multi-physics and multi-scalesystems. Key will be a convergence of artificialintelligence methods and first principle approachestypically used in MSO by laying down novelmathematical principles as the core language ofdigital twins.

Furthermore, the model hierarchies should › be able to (automatically) evolve with the availability

of new information, data, or even changes in theprocess,

› allow adaptive models and solutions with seamlesschoice of accuracy and speed,

› allow real-time and interactive simulation andoptimisation,

› be made robust towards inaccuracies in the dataand the model,

› be able to quantify the uncertainties and risks thatcome with the determined solutions,

› lead to the convergence of artificial intelligence andphysics-based models,

› exploitation new computing architectures, e.g.combined cloud - edge solutions,

› be flexible for new user interaction concepts,› allow the use of advanced black box solvers MSO

software packages,.

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Figure 2. High level schematicof this initiative and itsconnection to other initiatives

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Goal of the initiativeThe goal is to accelerate the development andoptimisation of industrial processes and devicesextending current Model-based Systems Engineering(MBSE) concepts to model-based assistance along thecomplete life cycle. What is needed is a high poweredmulti-disciplinary effort to bring mathematical MSOmethods together with techniques for the treatmentof big data and artificial intelligence methods as wellas to make them efficient on modern hardwareenvironments. All results should be made availablewithin a European Open Source Ecosystem9.

European Strengths In the development of high performance computerarchitectures, Europe was lagging behind, but due to new initiatives in the HPC and exascale area it isworking hard to become one of the world leaders. A similar effort is needed in the MSO area. Europe istraditionally (for many centuries) very strong inmathematics, much stronger than it is in the HPC orexascale area, but bridging the gap between thesestrengths and industrial challenges as put forward inthe Industry 4.0 initiative is a big challenge in itself.The situation is improving, as reflected by the fact that the MSO industry is focussing more and more inEurope, as exemplified by Siemens and Dassault whoare quickly building up their MSO product portfolios.However, much more is possible when a major andconcerted effort is developed to truly bridge theaforementioned gap, and unite the strengths ofEuropean mathematicians with Industry 4.0 and otherinitiatives of this kind to bring European industry tothe forefront.

Approach of the initiativeAcademia and industry should › focus on new generations of algorithms and

concepts combined with a focus on usability andtransfer (technology driven research programmes),

› overcome the boundaries between disciplines aswell as academic and industrial research bycollaborative, co-located projects, e.g. creating jointresearch labs of mathematical (or MSO) technologybetween industry and academia, favouring longterm relationships that ease the transfer oftechnology,

› develop new ways of collaboration of companiesand public-private partnerships, to achieve fasttrack transfer and to support the formation of start-ups, e.g. by promoting funding opportunities forfast-track transfer projects from basic concepts toindustrial scale solutions,

› promote new academic highly interdisciplinaryeducation programs, and increase/create newpossibilities for obtaining PhDs within a company inclose collaboration with academia in mathematics,

› develop new business interactions through models(product co-development) and enhanced customerexperience (embarked models, improvement ofdata assimilation), e.g. by enabling efficient R&Dvirtual interactions through multi-fidelity modelsowned by different parties, while protectingintellectual property.

Benefits for industries and businessopportunities There are large business opportunities in utilizing thepower of models in combination with massivecomputing capacities, the increasing availability of rich

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data sets, modern data analytics and ArtificalIntelligence techniques. This is, in particular, the casewithin industrial partnerships whenever modellingconcepts or hierarchical modelling need to be co-developed; mathematical MSO techniques becomethe cornerstone of predictiveness and innovativedesign.

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Reference

1 Siemens: Mindsphere White Paperhttp://www.plm.automation.siemens.com/global/en/topic/MindSphere-Whitepaper/8683/index.htmlNASA: The Digital Twin Paradigm for Future NASA and US AirForce Vehicleshttps://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20120008178.pdf

2 Gartner: Top 10 Strategic Technology Trends for 2018https://www.gartner.com/smarterwithgartner/gartner-top-10-strategic-technology-trends-for-2018/

3 Summary ofhttps://www.forbes.com/sites/bernardmarr/2017/03/06/what-is-digital-twin-technology-and-why-is-it-so-important/#1ef8f9802e2a

4 http://innovate.fit.edu/plm/documents/doc_mgr/912/1411.0_Digital_Twin_White_Paper_Dr_Grieves.pdf

5 GE: https://www.ge.com/reports/scientists-built-a-digital-twin-of-a-car-battery-to-make-it-last-longer/

6 ANSYS: http://www.ansys.com/products/release-highlights/digital-twin

7 ORACLE: Digital Twins for IoT Applicationshttp://www.oracle.com/us/solutions/internetofthings/digital-twins-for-iot-apps-wp-3491953.pdf

8 Engineering.com: Mission Impossible: The Digital Twin:https://www.engineering.com/DesignSoftware/DesignSoftwareArticles/ArticleID/15919/Mission-Impossible-The-Digital-Twin.aspx

9 See also recommendations in the final report of the ESFForward Look project on Mathematics for Industry:http://www.eu-maths-in.eu/EUMATHSIN/wp-content/uploads/2016/02/2010-Forward-Look-MathIndustry.pdf

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Industrial visions and innovationIn order to make the vision from the previous pages more concrete, here are some

statements from companies describing related applications and stakes.

ESIMICHELIN

NORSREPSOLSHELL

SIEMENSAKSELOS ECOMT

MAGWELSMART SAMPLE

VORTECH

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At its inception fifty years ago, CAE 1.0 (Computer AidedEngineering), together with CAD and CAM for Productdesign and manufacturing respectively, is part of PLM(Product Lifecycle Management). PLM covers overallproduct development and documentation, while CAEfocuses on engineering analyses and simulation ofvalidation testing.

Leveraging the exponential power of HPC (HighPerformance Computing) and ICT (Information andCommunication Technologies), CAE 2.0 further providesa powerful digital backbone to accelerate the Productdevelopment cycle by incorporating VirtualManufacturing and its impact on performance testing,including the details of the physics of materials, andtherefore delivering a physically representative ‘VirtualPrototype’ all the way to pre-certification, real or digital.

In the context of the Outcome Economy, in which thecustomer Product itself is not the only objective, wecannot stay at the level of the pre-certification stage ofthe Product. Rather, we must address the experienceand performance of the Product in its intended andactual operating environment. Building on our deepknowledge of the Physics of Materials complementedwith the new technologies now available in recent years

- including Artificial Intelligence (AI), Big Data, andInternet of Things we must change the way weapproach Manufacturing of Products and, importantly,in the Performance Management during the entireProduct lifecycle from launch to retirement.

It is also essential that we have an effective modeldevelopment and assembly CAE Platform to enable andcontrol the ‘Art of Modeling’ within proper‘circumstances and limits’, on which we can developCAE multi-model chains and processes to approach.

So the spectacular progress of AI (Artificial Intelligence)with Machine Learning (ML) and Deep Learning (DL),together with the Cloud and IoT (Internet of Things), aretransforming the innovation focus from the Productdevelopment phase (PLM) to the Product PerformanceLifecycle (PPL) in its operational phase, i.e. during its reallife without failures or recalls, targeting intelligent/ assisted/autonomous products, and managing predictivemaintenance up to retirement and decommissioning.

This present expectation for CAE 3.0 is a fundamental‘disruptive’ transformation into Smart Virtual Prototypingrequires an augmented digital representation of theProduct no longer in its ‘nominal’ certified state, ‘but ‘as

ESI

Embracing Smart Virtual Prototyping, Factory of the Future,Hybrid Twin™, and Product Performance in its full Lifecycle

CAE 4.0 disruptive challenges in the age of the Internet of Everything

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aged’, possibly damaged, and ‘as interacting’ in itsexpected operational environment in service, i.e.represented, immersed, animated and interactivelypiloted as its Virtual Twin in its Virtual Environment..

Now the new frontier of CAE 4.0 arises when the theorybased approach is updated by in-service ‘real life’ datafrom sensors and IoT. The Virtual Twin now becomes theHybrid Twin (“HT”), combining the ML enhanced datadriven model with the theory built Virtual Prototype(“VP”), for the best of both worlds.

Essentially limited to the Product development phase, the legacy PLM paradigm is waning, while the new “PPL”(Product Performance Lifecycle) is waxing. Thisfundamental evolution of the Product full lifecycle™ withits Performance follow up and the actionable HybridTwin ™ is at the core of the Smart Factory and of theIndustry 4.0 grand challenge and huge promises.

Scientific and Technological PerspectivesAs models involved in science and engineeringapplications become too complex (nonlinear coupledsystems of partial differential equations) their analyticalsolution is often compromised and, more specifically, inthose of practical interest involving complex geometries,models and boundary conditions. Fortunately,computers came to our rescue. However, computers areonly able to make very efficiently elemental operations.

Consequently, it was necessary to transform complexmathematical objects (derivatives, integrals ...) intosimpler objects {elementary operations {and at the sametime, to reduce the number of points and time instants at

which the solution of the model was searched and fromwhich the solution could be interpolated everywhere (inspace and time). Such procedure is known as numericalsimulation and constituted a true revolution at the end ofthe second millennium, being considered as one of thethree pillars of the 20th century engineering, beingmodeling and experiments (for model calibration andvalidation purposes) the other two pillars.

In the previous (third) industrial revolution \virtual twins"(emulating a physical system from the accurate solutionof the mathematical model expected describing it) weremajor protagonists, making accurate designs possible.Numerical simulation is nowadays present in most ofscientific held and engineering domains, making possiblethe virtual evaluation of systems responses, alleviatingthe number of experimental tests on the real system thatthe numerical model represents. however, usually virtualmodels (virtual twins) are static, that is, they are used inthe design of complex systems and their components,but they are not expected to accommodate or assimilatedata so as to be done dynamic data-driven applicationsystems. The reason is that the characteristic time ofstandard simulation strategies is not compatible with thereal-time constraints compulsory for control purposes.Thus, real-time control was ensured by techniques basedon the use of adapted representations of the system(adapted in the sense that they relate some inputs tosome outputs, encapsulated into richer models forHybrid Twin™.

Mastering the Hybrid Twin™ and associated technologies,platform and knowledge, will be a key success factor forthe digital transformation and sustainablecompetitiveness.

To give an example, the virtual homologation of tireson vehicles during their joint development phase hasan important potential in terms of improving speed to market and efficiency. For this to be successful, itrequires the availability of multi-partner simulationplatforms where individual models can be shared and coupled in an efficient way, while simultaneouslypreserving intellectual property rights. In additionpredictive capability must also be guaranteed by the adequate use of multi-fidelity models and theavailability of validation data. Furthermore suchcollaborative platforms could benefit importantly fromgeneral multi-criteria optimization capabilities. Thisapproach would clearly establish new standards for the automotive industry, and result in considerableefficiency gain for all the businesses involved.

A second opportunity lies in the constant improvementof models based on the collection & exploitation of reallife data, well beyond the present capabilities availablefor data assimilation. Models of different nature andaccuracy could be potentially combined to provide theright compromise between accuracy and efficiency.

The ultimate goal here is an increased predictive powerin the assessment of the performance of our products.Eventually, once integrated into vehicles, such modelswill provide drivers with enhanced driving experience,and in turn enrich the understanding of tire usages inB2C applications. In B2B applications, these models willenable fleet operators to manage operations moreefficiently, improving uptime through predictivemaintenance and maximizing value creation fromproduct designs better adapted to specific usages.

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Michelin

Advanced Modelling at the Service of Innovative Productsand Services

At the core of our tire design process is the quality of modelling. It not only underpins our longterm worldwide technological leadership, but it also can create short term economicopportunities derived from enhanced methodologies in the conceptualization of tires.

More generally models and data analysis support thedevelopment of innovative products. Multi scale andmulti-physics analyses enable the identification of new technologies and provide deeper understanding at the smallest of physical scales. In modelling,extreme computational performances are needed toaccount for the unusual level of heterogeneities in thetire structure. This in turn requires dedicated work indomain decomposition and high performancecomputing and ultimately, sensitivity analysis willbecome increasingly necessary to optimizeperformances in a challenging framework wheresophisticated contact states and complex material laws remain a challenge. In this way this initiative will strongly support the design of long lasting andenvironmentally friendly performances

Finally “Digital Twins” play a key role for Industry 4.0.With the help of simulation they allow for thedevelopment of a deeper understanding of

product/process interaction. This understanding, inturn, enables better preventive maintenance and theadaptation of production tools in order to optimizequality and efficiency. These technologies can be usedto support productivity improvement, all the way fromearly understanding and learning, up to real timedecision making processes. Supporting industry with a long lasting framework for industrial twinning wouldallow for the experience, sorting and deployment ofrelevant technologies for the long run, without theneed to change the working environment.

All these axes can lead to powerful scientific andtechnological advances that will ultimately deliverhigher competitiveness to a wide range of industries. In this domain, partnerships are both welcome andnecessary in order to generate significant value. Thisincludes connecting to both public research units andstart-ups.

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Currently, the Nors Group is present in 17 countriesacross four continents: Portugal, Spain, Brazil, Angola,Botswana, Namibia, Mozambique, Cuba, Mexico, USA,Turquey, Austria, Czech Republic, Slovakia, Romania,Hungary and Croatia, with around 3.650 employeesand a volume of business exceeding 1.5 billion Euros.

The automotive sector and its aftermarket business,repair and maintenance services, will work with a bigamount of data in an ongoing updated approach. Theexisting information, either company history as well as new scenarios for this fast-changing environment,for example the self-driving and connected carstechnology, will introduce new paradigms on theexisting models (for instance the almost absence of carcrashes will reduce some markets, the body parts sellout or the private automotive insurance) combinedwith external data will rise even more the importanceof tailor-made models, adapted to each businesschanging-realities.

For example, when sensors collect data from aconnected vehicle or device, the sensor data can be

used to update a virtual and digital copy of the realcar/truck/bus with the purpose of monitoring,diagnostics and prognostics the repair andmaintenance services. In this field, sensory data can becombined with historical data, human expertise andfleet and machine learning to improve the prognostics.

A digital twin is a digital copy of a real car/truck/bus,including its systems that synthesizes the informationavailable about the vehicle in a digital world. Thisallows any aspect of an asset to be explored through a digital interface, creating a virtual test bench toassess the safety and performance of a vehicle and its systems through its lifecycle and repair andmaintenance needs.

In a near future when the aftermarket servicesbusiness can access to the data that each vehiclegenerates and stores via telematics systems, building a digital twins platform, so each physical vehicle has adigital version, it will be a critical development to reachthe aim of the industry - reduce cost, improveefficiency and deliver value to the customer.

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Nors

Digital Twins in services Application in automotiveindustry aftermarket services

The Nors Group is a Portuguese group whose vision is to be a world leader in transport solutions,construction equipment and agriculture equipment. In its genesis are 85 years of history andactivity in Portugal, which started with the representation of the Volvo brand in 1933.

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In the energy sector, achieving technologicalcompetitiveness usually involves developing precisemathematical models and simulations of industrialprocesses, as well as designing methods for optimizingdecisions based on those simulation models.

Real industrial systems quite often involve modellingand solving complex coupled physical and chemicalphenomena which require important developmentefforts in order to produce outputs of simulations withan adequate predictive quality in a short amount ofcomputational time. In addition, these challengingsimulation models are tightly connected to decisionsconcerning supply chain, production plans, logistics andmaintenance that need to be optimized, thus resultingin big optimization problems with complex models atdifferent levels and scales.

Moreover, industrial equipment modifies itsperformance and operation during its lifecycle whilenew information is gathered from the physical domain,so mathematical models need to be adapted and

updated using historic offline and online data directlyfrom industrial operations. This issue is present in thewhole value chain of an energy supplier. To properlyassimilate all the available data, to integrate rigorousmathematical models with techniques in the field ofartificial intelligence and big data, and finally to takedecisions at various levels based on those simulationmodels in real time still remains a challenge.

In this context, obtaining knowledge by usingsophisticated simulations with adequate assimilation ofdata, aiming at real time decision making, will result inmore competitive, energy-efficient and environmentally-friendly operation of European industrial assets.

Achieving this goal will require an important effort in thefield of industrial mathematics, mainly aimed atproviding collaborative environments and platformsamong organizations in both industry and academia, aswell as initiatives bringing together mathematicalmethods with techniques in the field of artificialintelligence and big data.

Repsol

Industrial vision on Modelling Simulation and Optimization

Repsol is an integrated energy company committed to produce, transform and bring to marketenergy that is efficient, sustainable, and competitive for millions of people. Being engaged toinnovation, Repsol welcomes the European Commission proposal on the construction of an e-infrastructure for Mathematical Modelling, Simulation and Optimization.

Particularly in the initial phases of a product, device orprocess, a model-based approach is used asinsufficient data is available to support the manydesign decisions based solely on the data. Along thelife cycle, data abundance will increase and slowlydata analytics will gain prominence. Data analytics hasmade giant strides in the past decade and is findingits way into our processes.

However, we feel there is a need to strengthen theMSO community to allow us to accelerate theconception phase. This is particularly valuable in ourefforts to support the energy transition as well asexplore newer, greener chemistries. Many of thesystems we are exploring are inherently multi-scaleand require several different forces and drivers(mechanical, electrical, thermodynamic) to beassessed in an integrated fashion. These oftenconstitute complex, multi-scale, multi-physicsproblems. Brute force methods alone (HPC) will notbe sufficient. Only sophisticated, new mathematical

approaches, together with HPC and data assimilationwill be able to handle these problems.

Whereas in the past Shell largely relied on internalefforts to develop the technology it relies on, the last10 years we are partnering more and more with thirdparties from industry, service companies andacademia. The concept of a European Open SourceEcosystem, as described in this document, seems tous as the fastest route to innovation in the area ofcomplex multi-scale, multi-physics problems, andhence progress in the fields described above.

The concept of Digital Twins is very attractive. We arealready deploying them in several of our assets tooptimize operations and maintenance. Oncesufficiently powerful mathematical models areavailable as advocated above, we can move thispowerful concept into our labs as well. This wouldtruly give us the next generation laboratories that willdrive future progress.

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Royal Dutch Shell

Digitalisation in all its potential is rapidly gaining ground within Shell. Data analytics has anincreasing impact on our work processes, as more and more data is available. It adds value alongthe entire life-cycle of our products and processes. In addition, modelling, simulation andoptimization (MSO) are successfully and ubiquitously used throughout the various businesssegments of Shell.

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The company has roughly 372,000 employees – ofwhich 39,000 were newly hired in Fiscal Year (FY) 2017and of which 115,000 or 30,9% are based in Germany– working to develop and manufacture products,design and install complex systems and projects, andtailor a wide range of solutions for individualrequirements. For more than 170 years, Siemensstands for technological excellence, innovation,quality, reliability and internationality. In FY 2017,Siemens had revenue with business in more than 200countries of €83.05 billion. Arising from Siemenssoftware and digital services alone, €5.2 billion couldbe achieved (e.g. via MindSphere), making it a growthrate in this area of 20%.

Since 2007, Siemens is driving digital transformationwith $10 billion investment in U.S. softwarecompanies1 in the field of digital twins making it nowone of the largest computational engineering anddesign tool providers. Combined with its MindSphereoffering, no other IoT provider can drive closed-loopinnovation through complete digital twins forproducts, production, and performance like Siemens.

Digital TwinsA digital twin is a cross-domain digital model thataccurately represents a product, production processor performance of a product or production system inoperation2. The digital twin evolves and continuouslyupdates to reflect any change to the physicalcounterpart throughout the counterpart’s lifecycle,creating a closed-loop of feedback in a virtualenvironment that offers companies the best possibledesign for their products and production processes.Digital twins are the epitome of the digitalization ofplants and machinery – the virtual copy of a realmachine or system. And the twin is indeedincreasingly proving that it can help ensure optimizedmachine design, efficient commissioning, shortchangeover times, and smooth operation.

Siemens believes in a holistic approach that, withintelligent models and a closed-loop digital thread,leads to insight with actionable impact. Byincorporating multiphysics simulation capabilities, thedigital twin is a predictive analytics tool used todetermine the performance characteristics of

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Siemens AG

Siemens AG (headquartered in Berlin and Munich) is a global powerhouse in electronics andelectrical engineering. Operating in the fields of automation, electrification and mainly alsodigitalization, Siemens holds leading market positions in all its business areas.

products and production systems. The digital twin’send-to-end use can last through the design,manufacturing, operation, feedback, and updatesuntil the physical counterpart’s end-of-life. Productsand production systems can be consistently optimizedas the digital twin receives performance informationfrom the field (product) or the factory (productionsystem).

Example: Rethinking designSimulation-tools today are expert centric and requirelong cycle times. Thus simulation is very often usedonly lately during the design process and performednot by the designer or the domain engineer but byseparate simulation experts. These long iterativecycles lead to the fact that up to 80% of time-to-market is spent waiting3.

Novel mathematical approaches developed in the lastyears allow rethinking these paradigms4. Providingvery fast simulations tools, e.g. 3D mechanical orlumped systems simulations, allows interactivelyexploring design spaces manually or generatingdesigns automatically by means of mathematicaloptimization and machine learning. In particular foradditive manufacturing corresponding paradigmshifts are crucial, since available design spaces forproducts are exploding due to the disappearance ofmanufacturing constraints.

Apart from optimizing products and systems, inparticular digital twins allow to realize novel operationand service offerings build on engineering knowledgein terms of executable models. In particular for smalllot size products (e.g. gas turbines or large electrical

drives), fault detection, or operation close to thefeasible limit, artificial intelligence or statistic basedapplications are confined due to the available amountof data. Reusing existing engineering models in termsof digital twins allows addressing novel solutions andservices for these kinds of scenarios. Correspondingapplications are spanning the complete Siemensportfolio from large gas turbines to complete trains.At the same time Siemens is providing correspondinginfrastructure via its IoT operating systemMindSphere5.

Example: Reinventing operation of large drivesLet us consider an example of large drives6. If theywere repeatedly started, their interior temperaturecould shoot to as much as 800°C, thereby potentiallycausing serious damage. The motors must therefore

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A look through an augmented-reality headset at a motorallows a viewer to see an exact simulation of the motor in realtime and its interior with a real motor superimposed over it.

be allowed to cool before being restarted. Thetemperature in critical areas of the motors’ interiorcannot be directly measured. Normally, experts build ina safety buffer that rules out the possibility of damage.This frequently results in down times of up to 12 hoursthat are much longer than actually needed.

Technology leaps in the mathematical sciences allowtoday to reuse engineering models during operation.Using complexity reduction methods, correspondingmodels can be speed up by orders of magnitude,allows running a simulation parallel to the operationand by means of the simulation to estimatetemperatures in the rotor. The direction oftemperature changes can now be monitored in realtime and predicted. Such an optimized process thatcan prevent motor overheating and reduce thedowntimes required during the cool-off phase cansave up to €210,000 per hour.

The age of simulations and digital twins is just rising.According to the German Association for InformationTechnology, Telecommunications and New Media(BITKOM), every digital twin in the manufacturingindustry will have an economic potential of more than€ 78 bn by 2025. However, this potential can only beachieved if future systems are not only networked,but are also capable of seeing, understanding, andself-optimizing by building on digital twins in order toadapt to future changes7.

References:1 Siemens (2017): Siemens driving digital transformation with

$10 billion investment in U.S. software companies since 2007. Pressrelease.https://www.siemens.com/press/en/pressrelease/?press=/en/pressrelease/2017/corporate/pr2017030247coen.htm

2 Siemens PLM Community (2018): Digital Twin.https://community.plm.automation.siemens.com/t5/Digital-Twin/ct-p/DigitalTwin

3 Accenture (2012): Accenture Innovation and Product DevelopmentServices. https://www.accenture.com/gr-en/~/media/Accenture/Conversion-Assets/DotCom/Documents/Global/PDF/Strategy_1/Accenture-Innovation-Product-Development-Services.pdf

4 D. Hartmann, P. Stelzig, S. Gavranovic (2017): Accurate Interactive 3DEngineering Simulations Accelerated by GPUs. NAFEMS WorldCongress 2017https://www.nafems.org/downloads/presentations/nwc17/NWC17-509.pdf

5 Siemens (2017): MindSphere: The cloud-based, open IoT operatingsystem for digital transformation. Whitepaper.https://www.plm.automation.siemens.com/global/en/topic/mindsphere-whitepaper/8683

6 A. Barnard, S. Zistl (2018): Virtual Sensor opens a World of Efficiencyfor Large Motors. Pictures of the Future Siemens.https://www.siemens.com/innovation/en/home/pictures-of-the-future/digitalization-and-software/simulation-and-virtual-reality-virtual-sensors.html

7 Siemens (2017): Twins with potential. Digitalization in MachineBuilding. https://www.siemens.com/customer-magazine/en/home/industry/digitalization-in-machine-building/the-digital-twin.html

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The company has created the world’s fastest andmost advanced engineering simulation technology, toprotect the world’s critical infrastructure today andtomorrow. The technology has the power torevolutionise how we build and manage our criticalinfrastructure, and pushes the boundaries of whatmodern engineering and data analytics can achieve.Developed by some of the world’s best minds, theMIT-licensed technology builds something far beyondthe capability of a conventional digital twin – a DigitalGuardian that allows operators to not only monitor anasset’s condition in real time, but helps them to seethe future.

Challenges of Digital TwinsThe concept of a digital twin isn’t a new one; there arenumerous versions on the market. But they all haveone limitation in common – scale. Digital twins thatuse Big Data only are not capable of providingaccurate predictive maintenance, especially for criticallarge assets. For digital twins to achieve highpredictive power they have to be trained on a largeset of failure data, which is currently not available for

assets like FPSOs, oil rigs, and wind turbines. We needa physics-based take on Big data to achieve accuratepredictions of how assets behave in real life.

The science behind the traditional simulation tech –Finite Element Analysis – can’t model assets of a largescale in the level of detail needed to enable condition-based monitoring and predictive maintenance. Thescience behind Akselos’ technology changes this. Ithas the power to model assets of limitless scale. Thisleverages the power of the Industrial Internet ofThings for heavy industry in a way that has beenimpossible until now.

Benefits of Digital GuardianThe Digital Guardian is game changing technologythat combines engineering simulation software withsensors, machine learning and big data analytics tomonitor and protect large mechanical assets. It can dothis by creating a learning virtual replica of a structureor asset. The model, or Digital Twin, is calibratedbased on sensor data to create a Digital Guardianwhich will help structural engineers understand the

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Akselos

Top Predictive Power for Digital Twins

Akselos is a digital technology company headquartered in Switzerland, with operations inEurope, the USA and South East Asia. Akselos is powering digital transformation in heavyindustry with top predictive digital twins.

condition of the asset, and make predictions about itsfuture condition – allowing them to fix things beforethey break.

By using Digital Guardian technology, operators wouldbe making use of some of the most advanced digitaltechnology in the world to:› Gain entire visibility of the condition of an asset› Understand structural capacity to support Asset Life

Extension› Data that helps businesses make smarter, informed

decisions› What if? Virtual scenario planning› Optimize maintenance schedules enabling a move

towards zero unplanned downtime.

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During the past few years, cost reduction andtechnical access to technology and information havegained popularity through by the application ofdiverse techniques. The management of enormousquantities of data trough mathematical and statisticalalgorithms and heuristics. These tools have become astrategic element in our business which allows us tooffer highly competitive products and services. It is forthese reasons that the use of and proliferation ofthese tools and techniques in the industrial field is ofsuch relevance to ECOMT. Specifically, ECOMT hasbeen a very active participant in developing expertsystems such as OTEA software, whose inferencedrives employ statistical models or systems in otherneuronal or Bayesian networks which are especiallyuseful in the decision-making process in areas wherethe level of attention of qualified personnel may below, such as the use and maintenance of installationsof businesses with multiple site optimization ofenergy usage per installation.

Applying Artificial Intelligence, machine learning,classifying and data filtration, mining and othertechniques to solve regulation as well as controlproblems in the industry such as detecting anomaliesand defects are part of what ECOMT does for itsclients on a day to day basis. The creation of expertsystems of different range, generalizing conversionbots, applying advanced mathematics to solveoptimization problems, applying statistics forapplication ranging from the measurement of indirectmethods to classifying information, clustering orautomated resolution proposal of incidents anddecision making are areas in which our business isstrategically vested along with the need to collaboratewith public agencies and organisms who holdpertinent scientific knowledge derived from formalscience.

Given the nature and quantity of data provided by ourclients, it would not be possible to generalize the useof these methods and technologies without counting

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ECOMT

ECOMT (www.ecomt.net) is a company dedicated to the development of technology, softwareand services to control and manage the procedure, equipment and installation in the industrial,energy and logistics fields. Our ultimate objective is to help our clients to better manage andensure the most efficient use of energy. We provide the guidance and equipment necessary toguarantee a sustainable environmental economy of the business.

on the high-performance computing with which wehabitually work.

Finding public and private entities like thoseassociated to MATHS-IN with which to collaborate togenerate and increase the value for our clients and tofacilitate the transfer of technology and knowledgefrom our researchers to the industry is part of ourbusiness strategy.

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The results that are produced serve as input fordesign decisions for the object under development.The figure represents this high-level perspective. Overthe last decade a zoom-in of this figure shows thatthere exists a self-similar hierarchical substructure ofthe core modules. A core module is a collection ofsub-core modules that process subsets of problems.

Interoperability of a collection of sub-cores, dealingwith design challenges in the semiconductor industryhas become a key feature of MAGWEL's business. Theinterfacing between (sub-) cores requires thedevelopment of dedicated application-programminginterfaces (APIs), modifications of the (sub-) cores toaccess data structures inside the cores and upgradingthe core's states. With the increasing demands ofcomplexity it becomes critical to design the cores withhaving the interoperability already in mind. MAGWELhas applied above software model to electronic-designautomation (EDA) tools for development ofchips in the automotive industry, chips design for data

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MAGWEL

The key success of modeling simulation and optimization is found in the predictability level of theunderlying core modules that mimic the real world actors in a digital clone. The digitalrepresentation is composed from a series of ingredients. In a top-down perspective the coremodules require input data and generate results. At the input side there are the models which ina condensed way describe physical response to external stimuli. (See top graph of Figure1).

Figure 1. Self-similar MSO software design view.

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servers by combined compute kernels for theelectrical and thermal characterization of the chips.

Another area of application is the design of RF chipsfor near-field communication by coupling anelectromagnetic field solver with a circuit simulatorusing tight interfacing (holistic coupling) between thecores. More recently a similar approach we applied

for the development of the MAGWEL tool ESDi thatanalysis the chip's robustness against electrostaticdischarge (ESD) failure. The successes of theseapplications demonstrate that the APIs will play anincreasing important role in for the MSO practice. Theactual construction of APIs is a challenging task thatrequires combined expertise from mathematicians,software engineering and field-applicationengineering. However, once having the APIs in placetheir use increases the predictive power of the coremodules tremendously. In figure 2, a chip the layoutof an integrated circuit is shown. As an illustration, infigure 3 a typical result of a holistic coupled set of theelectrical and thermal core solvers is shown for a chipsection of which the layout is shown in figure 2.

Figure 3: Thermal map of the driver shown in Figure 2 (lower part).

Figure 2 View of a chip.

This sensational example reminds us that theacquisition of information has a cost, which shouldnot be overshadowed by the immense momentumacquired recently by scaled up data processingsystems, also known as « Big data ». Destructiveassays performed to develop novel materials, artificialevolution procedures executed to obtain enzymes ofindustrial interest, perturbations of a marketingscheme to assess the response of the demand, or theestimation of dose-response curves in thepharmaceutical domain are just a few moreillustrations of the diverse realities behind the termcost here. Irrespective of the modelling task at hand,the optimisation of spendings in data acquisitiontowards a maximal gain of information is paramountto securing the full benefits of advanced modellingand simulation techniques.

From a formal standpoint, it is essentiallystraightforward to follow the Bayesian paradigm anddefine a predictive information gain over the full

range of the control parameters governing thephysical counterpart of a digital twin, integrating theknowledge composing it and the data alreadyacquired. As more observations come in, its repeatedoptimization designates to the experimenter thevalues of the control parameters to be assessed next,resulting in the training effort to be concentrated oninformation-rich areas of the parameter space.

In practice, the construction of a Bayesian trainingscheme for a digital twin is a demanding expert taskspecific to the system under scrutiny. Yet, it results ina probabilistic abstraction of the training processwhere otherwise unrelated physical systems mayconverge, so that a limited number of algorithms maysuffice to guide the training of a broad range of digitaltwins.

The performance of such approaches dependscritically on sharing statistical strength locally in theparameter space, resulting in massive averaging

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Smart Sample

Over the past decade, medical imaging has been truly revolutionized by the development andadoption of compressed sensing, a methodology that enabled a drastic reduction of the numberof data points necessary for reconstructing the 3-dimensional shape of an organ or a tissue,thereby reducing patients’ exposure to radiations and demultiplying the number of examinationsin a day that can be performed with the same device.

operations that cannot be executed without carefullyoptimized algorithms, efficient programming andhigh-performance computational infrastructures.

The advancement towards a cost-effective training ofdigital twins will find its fastest pace within a networkof diverse players, who will be able to take advantageof the versatility of the mathematical methodsinvolved and to contribute jointly to the developmentof a solid toolkit.

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In the last years, we have noticed a convergence ofapproaches in the field of modeling and simulation.First of all, where modeling and measuring used to beseparate activities, the combined use of models andobservations is considered to be essential in manysectors. Secondly, we see that modern users put everhigher demands on the interaction with models: theycome to expect real time interaction and advancedgraphics, often through web-interfaces. But fancygraphics is obviously not enough: users also expectthe physics behind the simulation to be reliable.Finally, now that the initial hype in machine learning isover, many have come to realize that machinelearning and first principle modeling are synergetic:data science will not replace traditional modeling butwill augment it in very useful ways.

All these aspects come together in the concept ofdigital twins. This makes the digital twin an excellent

focus point for future developments.

The elements of digital twins are mostly there already:we have advanced first principle models for manyprocesses; we have wonderful graphics; we have awide range of data-assimilation methods and we arequickly learning to manage and analyze largedatasets. However, putting these elements togetherraises the issues such as those that are addressed inthe EU-MATHS-IN initiative. It will create a need forfaster models, it will put much stronger demands onthe data assimilation methods, it will heighten therequirements in terms of robustness and usability ofmodeling and simulation systems. Developing generictechnology to address such issues will provideimmediate benefits across many different industries.

An example of the potential benefits that we see is inthe utility sector. In distribution systems for water, gas

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VORtech

VORtechs mission is to assist our customers in developing the best possible modeling andsimulation facilities. Our customers come from a wide range of sectors, including watermanagement, oil and gas, the process industry, traffic management and environmentalmanagement. We see it as part of our mission to stimulate the development of new modeling-and simulation technology that will benefit our customers. As an SME, we do not have theresources to do or pay for research ourselves, but we can support cooperation betweenacademia and industry.

and electricity, there is a strong interest in having areal-time view of the entire distribution network withonline facilities to analyze events and with thepossibility to perform what-if simulations in themitigation of problems. In water distributionnetworks, the ability to quickly detect and localizepipe bursts is seen as important to avoid customercomplaints and to limit the damage from such anevent. Power distribution networks will come toexhibit a much stronger dynamic as renewable butfluctuating energy becomes a larger part of ourenergy supply. Being able to handle and manage thisdynamic is seen as a major challenge for powerdistribution companies. Given the complexity ofdistribution networks, things like these just cannot bedone without the technology that is proposed by theEU-MATHS-IN initiative.

Regarding the initiative as such, we feel that theinitiative should not only focus on research but makea real effort to make the results operational inindustrial settings. This is essential for making surethat the right knowledge is developed and that thetechnology that is developed is actually applicable inpractice.

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The value of mathematical sciences

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Mathematics, more specifically MSO (mathematicalmodeling, simulation and optimisation), is anessential asset for addressing tomorrow’s challenges:knowledge, innovation and competitiveness. Althoughthe excellence of European research in mathematicsis world renowned, its interaction with the industrialworld still lacks clarity. Yet, industry and the businessworld abound in mathematics more or less explicitly(models, statistics, algorithms, numerical simulation,optimization, etc.):

“The domains that mobilize advanced mathematics aretoday considerably more numerous than twenty yearsago. They are also more strategic. (...) Today we see newprofessions appearing and new economical models, inwhich statistics and data analysis play a major role. Thecollection, structuring, transformation and exploitation ofcollected data traverse high-level mathematical processes.(…) In the new paradigm, marked by the continuitybetween fundamental and applied mathematics and bythe presence of fundamental mathematics at the heart ofthe economical world, the question of communication iscentral.”

Jean-Pierre Bourguignon, President of the EuropeanResearch Council, « Un nouvel âge d’or pour lesMathématiques en entreprise ? » (2014)

This tendency has been confirmed by an ensemble ofreflections led over the past few years bymathematics communities all over the world. TheForward Look project of the Europan ScienceFoundation entitled “Mathematics and Industry” wascarried out in 2009-2010 (see page 40). Besides givinga number of important recommendations, this reportconcludes:

“The basic message of this report is that if Europe is toachieve its goal of becoming the leading knowledgebasedeconomy in the world, mathematics has a vital role toplay. In many industrial sectors the value of mathematicsis already proven, in others its potential contribution tocompetitiveness is becoming apparent. The benefitsresulting from a dynamic mathematics communityinteracting actively with industry and commerce areconsiderable and certainly far outweigh the rathermodest costs required to support such a community.

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The value of mathematical sciences (MSO) for the European economy

Nevertheless, such benefits will not be realised unlessaction is taken to develop mathematics and acoordinated community of industrial and appliedmathematicians needed for the future success and globalcompetitiveness of the European economy andprosperity.”

In the following sections, we give an impression of thepower of the mathematical sciences/MSO, with oftensurprising facts that are unknown to the larger public.

Studies into the economic value of themathematical sciencesIn 2012, 2014 and 2016, studies were carried out intothe economic value of the mathematical sciences inthe UK, The Netherlands and France, respectively.Summaries othe these reports are provided here.

UK report (Deloitte UK):“The report reflects the excellence of the UKmathematics research base, and the impressive andfar-reaching impact of the mathematical sciences. Thereport looked at mathematical science occupations,defined as occupations which either entailmathematical science research or which use tools andtechniques derived from mathematical scienceresearch. The report estimates the contribution ofmathematical science to the UK economy in 2010 tobe quite remarkable: 2.8 million in employment terms(around 10 per cent of all jobs in the UK) and £208billion in terms of Gross Value Added (around 16 percent of total UK GVA). Productivity (as measured bydirect GVA per worker) is significantly higher inmathematical science occupations compared to theUK average (approximately £74,000 versus £36,000),

and as such the direct GVA impact of mathematicalsciences research is proportionately higher than theshare of direct employment.

In addition to these direct impacts, mathematicalresearch activities by organisations and employeeshave impact across the supply chain (indirect effects)and also affect household spending (induced effects).There are also wider impacts and benefits generatedby organisations using the research. Sectorscontributing to this impact include Computer Services,Finance, Aerospace, Telecommunications, Researchand Development, Pharmaceuticals, PublicAdministration and Defence. The impact of dataanalytics, and its contribution to innovation and newinvestment, is particularly noted.”

Dutch report (Deloitte Netherlands):“The full time equivalent of about 900,000 highlyeducated employees use mathematical sciences inthe Netherlands. They include scientists who usemathematics all the time, as well as bankers, whospend some of their time computing the value ofassets, and physicians, who use maths to interpretmedical tests.These 900,000 jobs not only generate direct incomefor the employees involved. People who work inindustries that supply organizations wheremathematical sciences practitioners work and inbusinesses where these practitioners spend their ownincome benefit as well. Based on standard input-output analyses of the Dutch economy, theseso-called indirect and induced effects are estimated tocreate another 1.4 million jobs, resulting inmathematical sciences contributing for up to 26% to

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total employment. Because these are high incomejobs, the economic contribution of mathematicalsciences is even higher, representing around 30% ofDutch national income.”

French report (CMI):“This study emphasizes the very strong and growingimpact of mathematics for the competitiveness andgrowth of the French economy:› The jobs affected by mathematics have a strong

added value (15% of GNP and 9% of employment)and are increasing in number (+0.9% per year from2009 to 2012 vs. +0.5% for overall employment)

› It turns out that 44% of key technologies, identifiedas such by government reports, are stronglyaffected by progress in mathematics.

› The mobilization of 5 major competency fields ofmathematics (signal and image analysis, datamining, modelling-simulation-optimization (MSO),high performance computing (HPC), computersystem security and cryptography) will increase innumerous activity sectors, in particular energy,health, and telecommunications.

The employability of mathematics students isexcellent: businesses (both large ones and SME’s) areprogressively becoming aware of this impact but arestill somewhat ill-organized for managing in-housemathematical expertise.”

The correlation of mathematical skillsand country competitiveness

A strong mathematical sciences foundation is criticalto the success of any advanced economy. Bettermathematical skills correlate with a more competitiveeconomy and a higher standard of living. Moreover,with the revolutions in computational science, bigdata, statistics and business analytics the importanceof mathematical sciences to society is likely toincrease substantially in the coming decades. Theserevolutions are driven by ever more powerfulcomputers, the data explosion, and improvedalgorithms (see next section).

The World Economic Forum describes three types ofcountries: factor-driven economies which compete onlow-skilled labour and natural resources (like Angola),efficiency-driven economies which rely on goodeducation and well-functioning markets (think ofBulgaria) and innovative economies where businessesmust compete with new products, technologies,processes and business models. These economies,many of them in Europe, require an exceptional levelof sophistication to maintain their high standard ofliving.

The Figure on the next page shows the relationbetween the mathematical abilities of pupils percountry, as measured by the OECD in its PISA study,and the Global Competitiveness Index for that countryas defined by the World Economic Forum. The mostcompetitive nations generally have populations withstrong mathematical skills.

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The power of MSO in comparison withMoore’s LawAlgorithms outperforming machines

Everyone knows Moore’s Law, stating that the numberof transistors in a dense integrated circuit doublesapproximately every two years. As more transistors fitinto smaller spaces, processing power increased andenergy efficiency improved, all at a lower cost for theend user. This development not only enhancedexisting industries and increased productivity, but ithas spawned whole new industries empowered bycheap and powerful computing.Less known or even virtually unknown, at least to non-experts, is that the development of (mathematical)

algorithms has shown a development similar to thatof Moore’s Law, and in all cases it turns out thatalgorithm improvement outperforms machineimprovement, sometimes by significant factors. Thefollowing figures prove this statement for variousareas in mathematics: solution of linear systems (acore activity in all simulation software), methods foroptimisation (both the traditional linear programmingand the more recent mixed integer programmingmethods), and methods using particle simulations (tostay closer to the physical formulation).

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Figure 1: Relation between mathematical ability and country competitiveness

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0 5 10100

102

104

106

108

15

Number of Years

Improvements in Algorithms Relative to Moore’s LawRa

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f Inc

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e in

Pro

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ing

Perf

orm

ance

Banded GE

Gauss-SeidelMoore’s Law

Optimal SOR

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Type of algorithm:

CG Conjugate GradientGE Gaussian EliminationGS Gauss-SeidelMG MultigridSOR Successive Over Relaxation

Full MG

20 25 30 35

0

Figure 3. Algorithm improvement in the area of LinearProgramming (optimisation)

Progress in LP: 1988-2004(operations Research, Jan 2002, pp. 3-5, updated in 2004)

Algorithm (machine independent): 3,300xPrimal versus best of Primal/Dual/Barrier

Machines (workstations –> PC’s): 1,600xNET: Algorithm × Machines: 5,300,000x

(2 months/5300000~=1 second)

Figure 5. Algorithm improvement in the area of Mixed IntegerProgramming (optimisation)

Overall improvement: 1990-2014Algorithm: 870,000xMachines: 6,500xNET: Algorithm × Machines: 5,600,000,000x

(180 years/56B~=1 second)

Figure 2. Algorithm improvement for solving linear systems Figure 4. Algorithm improvement for particle simulations

Applied mathematics research forexascale computingRecommendation: invest in applied mathematicsresearch

A few years ago, the US Department of Energy (DOE)asked a working group of renowned researchers fromacademia and industry to report on the needsregarding applied mathematics research for exascalecomputing. In March 2014, this report was published.

Quoting from the executive summary:“High fidelity modeling and simulation of physical systemsis a critical enabling technology area for the U.S.Department of Energy (DOE), required for addressingsome of the most challenging problems in energy, theenvironment and national security. The importance ofcontinued advances in this area cannot be overstated. As a result, DOE is aggressively pursuing an exascalecomputing program that includes applied mathematicsresearch focused on the unique challenges andopportunities present at this scale.”

The report contains a detailed study of the needs withrespect to applied mathematics, and also containsnumerous examples of fields where progress needs tobe made. The necessary actions are summarized infive key recommendations, associated with anAdvanced Scientific Computing Research Program tobe set up:1. The Advanced Scientific Computing Research

Program should proceed expeditiously and withhigh priority with an exascale mathematicsinitiative so that DOE continues to lead in usingextreme-scale computing to meet importantnational needs.

2. A significant new investment in research anddevelopment of new models, discretizations, andalgorithms implemented in new science applicationcodes is required in order to fully leverage thesignificant advances in computational capabilitythat will be available at the exascale. Many existingalgorithms and implementations that have reliedon steady clock speed improvements cannotexploit the performance trends of future systems.

3. Not all problems require exascale computation,

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and yet these problems will continue to requireapplied mathematics research. Thus, a balance isneeded in the DOE Applied Mathematics Researchportfolio that provides sufficient resources torealize the potential of exascale simulation whilepreserving a healthy base research program.

4. An intensive co-design effort is essential forsuccess, where computer scientists, appliedmathematicians, and application scientists workclosely together to produce a computationalscience discovery environment able to exploit thecomputational resources that will be available atthe exascale.

5. The Advanced Scientific Computing ResearchProgram must make investments to increase thepool of computational scientists andmathematicians trained in both appliedmathematics and high-performance computing.

Future and emerging mathematical technologiesfor EuropeIn December 2017, a workshop was held at theLorentz Center in Leiden, a national center forinternational workshops in all scientific disciplines.The guiding philosophy is that innovative researchthrives on interaction between creative researchers.Lorentz Center workshops focus on newcollaborations and on interactions in highly diversegroups of researchers – international and withdifferent scientific viewpoints as well as seniority,gender, and culture.

For the workshop held from December 11-15, 2017,the aim and objectives were formulated as follows:

“The current and future technological and economic

development of the industrial Europe is characterizedby a steadily growing complexity of modern productsand processes, as well as ever shorter innovationcycles. Principal issues which must be addressed arethe scarcity of resources, recycling, climate change,assessment of the risks to the environment andsociety, as well as increased automation and a holisticview of the life cycle of a product. The long-term andsustainable solution to these problems is onlypossible through an intensive support of the

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Scientific Organizers

• Data Based Modeling• Adaptivity in Space, Time and Model• Multiphysics and Multiscale Modeling• Model Order Reduction• HPC Methods in Simulation and

Optimization• Uncertainty Quanti�cation and Risk

Analysis• Systems Analysis and Networks

Topics

11 - 15 December 2017, Leiden, the Netherlands

Future and Emerging Mathematical Technologies in Europe

Image: a Finite Element Mesh of Europe which could be used for computational simulation and optimization methods.

Poster design: SuperNova Studios . NL

The Lorentz Center organizes international workshops for researchers in all scientific disciplines.

Its aim is to create an atmosphere that fosters collaborative work, discussions and interactions.

For registration see: www.lorentzcenter.nl

• Zoltán Horváth, SZE Győr• Volker Mehrmann, TU Berlin• Wil Schilders, TU Eindhoven• Evgeny Verbitskiy, Leiden U• Kees Vuik, TU Delft

development procedures of new products andproduction processes via a holistic mathematicalModeling, Simulation and Optimization (MSO)approach, where in each case parallel to each productor process a virtual product or process (the digitaltwin) is generated. On this basis a simulation offunctionality and design, as well as of long-termeffects and risks, one is able to design optimizedproducts and sustainable process controls. In additionto the classic areas of mechanical and vehicleengineering in which a modularized and component-based development on the basis of mathematicalmodels is already established, this approach is alsoessential in the development of Industry 4.0 as a keytechnology and a decisive competitive advantage. Thisprocedure also plays a central role in all other fields ofscience, economy and society and the aim must be tostrengthen the leading position of Europe in thissystem- oriented approach. Success of the abovementioned approach relies heavily on the furtheradvancement of Mathematical Technologies.Mathematical Technologies play already an essentialrole in almost all areas of industrial and societalrelevance. As numerous success stories show,Mathematical Technologies, in particular Modelling,Simulation and Optimization tools, provide real andproduction processes, analysing data, enabling virtualprototyping of new products and reducing costs.Mathematical Technologies find application in a widerange of scientific and technological fields, and it isexpected that in the coming years, with the increaseduse of technology and availability of ever morepowerful high performance computers, the impact ofMSO tools will become even more significant.There is a clear need to bring together the existing

European National Networks of Research Centres for Industrial and Applied Mathematical Technologies,to ensure a common effort towards one main andshared objective: providing the industrial andscientific communities with a single coordinated andcomprehensive infrastructure for MathematicalModelling, Simulation and Optimization, and resultingresearch programs.The workshop is organized under the auspices of EU-MATHS-IN – a European Network of Mathematicsfor Industry and Innovation. This network is acollaboration of national organizations from 17European countries. The promoting partners of EU-MATHS-IN are the European Mathematical Society andthe European Consortium for Mathematics in Industry.The primary objective of the meeting is to discusssuccess stories and share experience and bestpractices of organizing collaborative research projectswith industry, as well as to discuss and brainstormabout joint future activities. One of the majorobstacles to be addressed is the low visibility ofmathematical technologies in European programs. We will also discuss measures facilitating awarenessabout existing expertise in Europe and knowledgetransfer.”

Mathematics: engine of the economy(original German title: Mathematik: Motor derWirtschaft)During the Year of Mathematics in Germany (2008), a workshop was held in the Oberwolfach MathematicsResearch Institute where 20 captains of industrypresented their view on the importance of mathematicsfor their companies. The resulting book “Mathematik -Motor der Wirtschaft” came about in close cooperation

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between the Oberwolfach Foundation and theMathematisches Forschungsinstitut Oberwolfach andfeatures articles by renowned business figures. It waspresented by the German Federal Minister of Educationand Research, Annette Schavan, at a gala event. In theirarticles, various heads of major German companies -Allianz, Daimler, Lufthansa, Linde, and TUI, to name but a few - sum it up in a nutshell: Mathematics iseverywhere, and our economy would not work withoutit. SAP's CEO, Henning Kagermann, puts it like this:"Corporate management without mathematics is likespace travel without physics. Numbers aren't the be alland end all in business life. But without mathematics,we would be nothing." The list of authors in theSpringer book reads like a Who's Who of German DAXcompanies. The book (in German, except for onecontribution in English) is published by Springer VerlagHeidelberg.

ESF Forward Look project “Mathematics andIndustry”In 2009-2010, a Forward Look project of the EuropeanScience Foundation was undertaken to investigate therole of mathematics for industry. The project issued 2reports, viz. a report with recommendations andfindings, and a book of success stories:

The second recommendation readsIn order to overcome geographical and scientificfragmentation, academic institutions and industrymust share and disseminate best practises acrossEurope and disciplines via networks and digital means.

Roadmap implementation:› Researchers in academia and industry must adapt

their mentalities to the different mathematical andscientific domains they interact with. anddisseminate best practises.

› The mathematical community in collaboration withindustry should create a journal devoted toindustrial mathematics and contribute to aEuropean Digital Mathematics Library.

› Academic institutions and industry must facilitatethe employment mobility between academia andcompanies.

› The mathematics community and industry shouldwork together on real opportunities inapplicationthemed competitions.

and has led to the foundation of the organisation EU-MATHS-IN (http://www.eu-maths-in.eu) whosemission is “to leverage the impact of mathematics on innovations in key technologies by enhancedcommunication and information exchange betweenand among the involved stakeholders on a Europeanlevel.”

The first recommendation reads:Policy makers and funding organisations should jointheir efforts to fund mathematics activities through aEuropean Institute of Mathematics for innovation.

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Roadmap implementation:› EU and National funding agencies should

coordinate cMsters of excellence in industrialmathematics and create a European Institute ofMathematics for Innovation (EIMI) formathematicians and users of mathematics.

› EU and European governments should set up aStrategy Taskforoe for Innovation and Mathematics(STIM) in order to develop a European strategy formathematics.

› Policy makers should put in place a Small BusinessAct in Mathematics (88AM) to encourage spimoffcompanies explicin using mathematics.

› EU must identify industrial and appliedmathematics as an independent crosscuttingpriority for the Framework Programme 8.

This remains a very important recommendation, alsoin view of the previous sections where the importanceof mathematics for European competetiveness andprosperity is demonstrated.

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COLOFON:

Foundation EU-MATHS-INEuropean Service Network of Mathematics for Industry

Correspondence address:Frankische Driehoek 365052 BM GoirleThe Netherlands

Email: secretary@eu-maths-in.euwww.eu-maths-in.eu

Design: WAT ontwerpers

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