modeling, simulation and optimization of real-world ...lila/files/belgrade... · dfg research...

DFG Research Center MATHEON Mathematics for key technologies

Modeling, Simulation and Optimization

of Real-World Processes: New Mathematics

for Key Technologies

Volker Mehrmann

Serbian Academy of Science and Art Belgrade, June 2012

DFG Research Center MATHEON

Mathematics for Key Technologies


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MATHEON Drives Innovation


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MATHEON and its Institutions

Freie Universität Berlin (FU)

Humboldt-Universität zu Berlin (HU)

Technische Universität Berlin (TU)

Weierstrass Institute for Applied Analysis and Stochastics (WIAS)

Zuse Institute Berlin (ZIB)


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The MATHEON vision

• Mathematics is one of the keys to key technologies. Its potential

has not yet been brought to bear. The aim of MATHEON is to

profoundly change this situation.

• The development of key technologies is characterized by two

tendencies: while innovation cycles get shorter and shorter their

complexity is getting higher and higher.

• High complexity is best treated by a high degree of abstraction.

The language of abstraction is mathematics.

• But Mathematics is not only a language, it adds value:

Theoretical insight, efficient algorithms, optimal solutions.


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A: Life Sciences

C: Production

D: Electronic and Photonic Devices

E: Finance

F: Visualization

ZE: Education

B: Networks

Application Areas & Mathematical Fields

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Scientific Structure


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Our Competence

Scientists of MATHEON

members 230

Project heads 64

DFG-financed researchers 66

PhD students 71

professors 48

current number of projects 55

Most members from applied mathematics!

Date: May 2012


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Financial Resources

Spent MATHEON funds (in million €) in 2011

(total of 20,3 million €)

Industrial third party

Other third party public

DFG / personnel

DFG / consumables

DFG / central management

Inst. Core Support personnel

Inst. Core Support consum.


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Quality of a running project

Publications, plenary talks,

etc.

Additional funding

Networking (cooperations, ext./internal)

Visibility / outreach

Relation to applications a/o industry S

cientific

Exce

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Key T

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(Internal) Quality Management: Criteria


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9 collaborative research centers (DFG)

10 priority program (DFG)

2 research units (DFG)

2 research training groups (DFG)

2 grad. schools: "Berlin Mathematical School“ and "Berlin School of

Regenerative Therapies“

1 int. Max-Planck research college "Comp. Biology and Scientific Comp.”

1 Marie Curie Initial Training Network (EU)

3 ERC Advanced Grants, 2 ERC Starting Grants, 1 Russian Megagrant

PVcomB - Competence Centre Thin-Film- and Nanotechnology for

Photovoltaics Berlin (BMBF)

Numerous other collaboration projects

Cooperation with science and engineering


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Industry cooperation – examples

BASF, Bayer-Schering, Merck, Sanofi-Aventis, ...

Siemens, IBM, Infineon, Microsoft, NEC, Philips, ...

Deutsche Telekom (T-Systems), E-Plus, ...

DaimlerChrysler, BMW, Volkswagen, Tebis, Bosch, Nippon Steel, ...

Deutsche Bahn, BVG, IVU, Lufthansa, ABB, ADAC, Herlitz, ...

EdF, Open Grid Europe, DREWAG, Vattenfall (VEAG), Ruhrgas, BHP Billiton, ...

AMRO Bank, Bankgesellschaft Berlin, Commerzbank, Deutsche Bank London, IKB, Reuters Financial Software, ...

Numerous small and medium enterprises (SME)

Industrial Cooperation


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1000shapes GmbH (www.1000shapes.com): statistical shape models

Indeed Visual Concepts (www.amiravis.com): 3D data visualization (Amira), today: Mercury

JCMwave (www.jcmwave.com): Simulation software for nano-optical components

atesio (www.atesio.de): Plan, configure, and optimize telecommunication networks

Löbel, Borndörfer & Weider GbR (www.lbw-berlin.de): Optimization and consulting for public transport

Synoptio (www.synoptio.net): Mathematical consulting and software

Lenné 3D (www.lenne3d.de): Digital botany and real-time landscapes

inbion GmbH (inbion.math.fu-berlin.de): Bioinformatics solutions for life sciences

getLig&tar (www.getlig.com): drug design

molConcept GmbH (www.molconcept.com): molecular design & drug design

Spin-Off Companies


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A – Life Sciences


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InnoLab „math for diagnostics“: Proteomics

Aim: Development of novel diagnostic tools for early lung cancer detection based on proteomics fingerprinting Methods: Enhanced noise reduction, peak detection and identification of sensitivity-optimal fingerprints via novel robust filtering and dimension-reduced Bayesian classification techniques

C. Schütte (A19)


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InnoLab „math for diagnostics“: Angiology

Aim: Development of a non-invasive diagnostic tool for detection of cardiovascular pathologies (e.g. stenoses und aneurisms). Methods: Data acquisition via novel devices for multi-channel measurement; novel Bayesian classification techniques based on cardiovascular system model

C. Schütte (A19)


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InnoLab „math for diagnostics“: Pharmacokinetics

Aim: Development of new HIV long-term therapies that prevent drug resistance Methods: Compute optimal switching times between different drug combinations to avoid that resistant virus is archived; based on detailed model of virus kinetics and mutation

C. Schütte (A19)


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IT Companies Device manufacturers

Hospitals Research Groups

InnoLab „math for diagnostics“: Partners

C. Schütte (A19)


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Toxicological Appraisal of Micropollutants

Example: Prediction of estrogenic affinities & activities in drinking

water

Cooperations with industry:

BMBF: TransRisk

Simulation of binding processes Mathematics: Entropy estimation, to the estrogen receptor affinity, interaction models

M. Weber, V. Durmaz, R. Becker, S. Esslinger, 2009 M. Weber, K. Andrae, 2010 V. Durmaz, M. Weber, R. Becker, 2011

measured affinities

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M. Weber (A19)


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Mathematical Systems Biology

Development of a mathematical model for the human menstrual cycle

Cooperation Partner: Pfizer R&D, Sandwich, UK Duration: 04/2009 – 09/2011

Publications: S. Röblitz, C. Stötzel, P. Deuflhard, H.M. Jones, D.-O. Azulay, P.H. van der Graaf, S. W. Martin, ZR 11-16, Submitted. T. Dierkes, M. Wade, U. Nowak, S. Röblitz, ZR 11-15

• Modelling • Simulation (integration of stiff ODE/DAE and discrete stochastic systems) • Parameter identification (Gauss-Newton methods for nonlinear problems)

Problem: How does administration of gonadotropin-releasing hormone analoga influence the cycle?

Results: • 33 ODEs, 114 parameters • Prediction of hormone profiles and delay of ovulation • Software BioPARKIN

S. Röblitz (A18)


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Paradigm of virtual medicine

Real patient

Virtual patient

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2D segmentation via 3D

classification of known patient data adaptation of new CT stack

Statistical shape analysis

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Orthopedic surgery

Modeling, Simulation and

Planning of Orthopedic Surgery

Optimal design of facial implants Bilevel optimal control problem

Numerical implementation on patient-specific geometry

Efficient Algorithms Adaptive time integration

Domain decomposition + multigrid

Dynamical heterogeneous modeling 3d nonlinear contact mechanics

1d Cosserat rods

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Cranio-maxillo facial surgery planning

before operation / after operation / overlay

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B - Networks


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Gas Transport

Challenges in the Optimization of Gas Transport

• Gas transport itself

• Gas network capacity planning

• Gas storage

• Legal deregulation rules of the gas transport market

• Price fluctuations

• Seasonal fluctuations

• Development of required mathematical solution technologies

• .....

M. Grötschel, R. Henrion, T. Koch, W. Römisch (B20)


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• Modeling: network, flow, prices, weather, ....

• Simulation: network, flow, prices, weather, …

• Optimization: discrete/continuous, mixed-integer, stochastic, non-linear

Gas Transport: Mathematical Challenges



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Gas Transport: Research

since 08/2010: Open Grid Europe (OGE)



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Airline network revenue management

• A stochastic programming model for airline network revenue management

based on passenger scenario trees was developed.

• Passenger scenario trees are generated by employing historical data.

• The optimization model is solved by Lagrangian relaxation based on

dualizing leg capacity limits, bundle subgradient methods for the dual

and a Lagrange heuristics exploiting the small duality gap.

• The approach is applicable to mid-size Origin&Destination networks.

The test instance contained 54 O&D itineraries, 27 legs (airplanes),

time horizon with 23 data collection points, 1.441 nodes of the scenario

tree and, thus, totally 3.473.377 mixed-integer variables

and 2.774.445 constraints.


27 W. Römisch (B6)

In cooperation with Lufthansa Systems Berlin


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Siemens MSO

Cooperation with department

Modelling, Simulation and Optimization

Optimal planning of water networks

Placement of roboter in circuit board production

Study request for mathematical optimization

T. Koch (B20)


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Elevator group performance is crucial in today‘s high-rise office buildings

Elevator vendors introduced destination hall-call systems where each passenger

registers his target is assigned to an floor separately elevator in turn

more information and control opportunities

asked MATHEON to help develop advanced algorithms

Up to 120% more passengers served in the same time, with the same service quality in high-load traffic

Now implemented by

Advanced Elevator Control

M. Grötschel (B14)


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Integrated bus rotation and crew duty planning

Bus rotation planning = multicommodity flow problem (MFP)

Crew duty scheduling = set partitioning problem (SPP)

Integrated planning = MFP + SPP + coupling

Lagrangean relaxation, bundle method (LP), rapid branching (IP)

7 depots, 4 000 trips, 200 vehicles, 250 duties

BMBF Mathematics in Industry, integrated in ivu.plan suite

uvtdyxDyCxbByAxydxc t

uvd

TT ,,}1,0{,;;;1;min

IS-OPT: Integrated Bus & Crew Scheduling

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50

Actual IS-Opt

- 13,79 %*

number of duties

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Actual IS-Opt

- 5,88 %*

number of vehicles

R. Borndörfer (B15)


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Bus + aircraft rotations = multicommodity flows (solvable)

Train rotations = multicommodity hyperflows

Min. # vehicles, s.t. train composition, regularity, maintenance

Train compositions = hyperarcs (new), column generation

NP-hard (not approximable), but good extended formulation

1 week, 500 trips, 20 train types, 3*104 nodes, 5*107 hyperarcs

MATHEON B22 (1*hyperflows) + DB (2*implementation)

VR-OPT: Vehicle Rotation Planning for Railways

uvdxtsvvxdvvxvxxc d

uv

ddT ,}1,0{;,1))((;))(())((;min

R. Borndörfer (B22)


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Traffic optimization on the Kiel Canal

Connects North Sea and Baltic Sea

280 nautical miles saved compared to the way around Skaw

Canal with highest traffic in the World

R. Möhring (B13, B25)


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Opposing traffic creates problems

Ships must be scheduled to wait in sidings

Waiting can‘t be too long

New ships arrive online

Combines routing and scheduling

Very hard for MIP models



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Goals of the project

Improve manual planning

Recommendations for canal enlargement (widening, new sidings …)

Automated guidance during construction phase



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Steel Slab logistics

steel slabs arrive from casting

intermediate storage on stacks

further processing or delivery

different orders

transport by cranes or vehicles

scheduling = sorting with stacks

R. Möhring (B24)


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C - Production


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Mean-risk optimization of electricity portfolios


37 W. Römisch (C7)

Operation of a municipal power utility

Free (=parameter-free) shape optimization of air/exhaust flow channels in engines.

• Optimization Goals:

o Uniform outflow at outflow (turbo engine).

...velocity; ...average velocity at inflow.

o Alternatively: Minimization of the total pressure loss.

• Constraints to be considered:

o construction space; inflow (given position + flow profile), position of outflow boundary.

• State system:

o Stationary 3D Navier-Stokes-system with specific lateral boundary conditions.

Shape Optimization in the Automotive Industries

Sketch.

38 DFG Research Center MATHEON

38 M. Hintermüller (C11, 28, 31) in coop. w/ BMW Motoren GmbH and MathTech

Shape Optimization in the Automotive Industries

Reduction of objectives: 5-15% relative to initial configuration (shape from engineering-CAD-CFD-development)

Implemented modules (OpenFoam, STAR-CD CCM+)

Navier-Stokes-System

Adjoint-System

Shape Gradient

Remeshing

Graphic. after 60 iterations.


39 M. Hintermüller (C11, 28, 31) in coop. w/ BMW Motoren GmbH and MathTech

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Adaptive solution of parametric eigenvalue problems for PDEs

Industrial application Optimization of interior acoustics Fluid-structure interaction Large scale eigenvalue problems (N> ) Problem Most of the CPU-time is spent to solve eigenvalue problems Solutions Application of iterative eigenvalue solvers Use mesh adaptivity to reduce the size while maintain accuracy Balance the modeling, the FE and the iteration error Make use of modern computer architectures

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40 C. Carstensen (C22)

Typical instance:

• production line

• 4 robots in a work cell

• 50 weld points on a car door

Questions:

• Which points does each robot weld? (task assignment)

• In which order? (sequencing)

• What is the fastest and collision-free trajectory between two points? (path-planning)

At the moment:

Task assignment, sequencing and path-planning for all robots are done by hand.

Automatic reconfiguration of welding cells


41 D. Hömberg, M. Skutella (C30)

Automatic reconfiguration of welding cells

MATHEON Approach:

Combine discrete and continuous optimization

• Trajectory planning for robots avoiding collisions • Represent robots and obstacles as finite unions of polyhedra • Allows collision detection using linear programming arguments

• Graph representation for each robot: • Nodes: weld points that can be visited • Arcs: paths between two weld points • Each arc has a fixed and predefined travel time

In cooperation with Rücker EKS GmbH, Weingarten


42 D. Hömberg, M. Skutella (C30)


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D – Electronic & Photonic Devices

Computational Nano-Lithography

Source mask optimization in computational lithography

Real-time inverse scatterometry

Photomask Aerial image

Optimized process window

Phase grating

Electric field

Correlation of reconstructed parameters

[J. Pomplun et al. SPIE (2010)] [B. Kleemann et al. SPIE (2011)]


44 F. Schmidt (D23)

Computational Photovoltaics

Challenge: Increase efficiency of industrially produced thin film solar cells from currently < 9% to 13%.

Efficiency enhancement by rough surfaces


45 F. Schmidt (D23)

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Global photonic programs

US: Harnessing Light II – Photonics for 21st Century Competitiveness

EU: “Strategic Research Agenda – Lighting the way ahead“ (2010)

Germany: Photonik 2020 (2010)

Nano-optical components

Model optical structures with size comparable to wavelength

Exploit nano-scale effects like plasmonic waveguiding and plasmonic resonances

Combine effects to form functional units

Optimize the structures

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Circular grating resonator, cf. biomedical sensing

Optical fields in a thin film solar cell layer

Material-light interaction

Linear and nonlinear interaction

Interaction of electronic and optical properties

Using model hierarchies: classical models, semi classical models, quantum models

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Example Left: Classical model of plasmonic field (wrong) Right: Semi classical hydro- dynamical model (coincides with experiments)

Material-light interaction

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Semiconductor laser devices for optical communication

•Modeling and analysis of nonlinear material–light interaction •Multiscale structure of devices •Complex dynamical behavior

Different dynamical regimes in a mode-locked quantum-dot laser

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Nonlinear Optics: Pulse propagation

Maxwell equations for fields Nonlinear material response for fibers

Controlling Light by Light with an Optical Event Horizon

Physical Review Letters 106, 163901 (2011)

Challenge Controlling light by light in time and frequency

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Nonlinear optics: All-optical transistors

Switching

Weak control pulse

Strong signal pulse

Propagation model

provided by

MATHEON

Fundamental research leads to a novel technological concept!

Statistical optics

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Example: Yablonovitch limit 4n2 in ray optics limit What is the transition to wave optics?

qualitative influence on the

optical field

Statistical properties of sources in space and time

Statistical properties of media in space


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E - Finance

Trading in Illiquid Markets

Traditional financial market models assume that all trades can be settled at prevailing prices without market impact

Large investors usually move prices in an unfavorable direction

Alternative trading venues allow for a reduction in market impact

Objectives of various projects with Deutsche Bank AG:

• Mathematical models for liquidating large portfolios under market impact

• Optimal display strategies for iceberg orders

• Optimal order routing between primary and alternative trading venues (crossing networks, dark pools)

• Reduced form models of limit order books

• ...


54 U. Horst (E2)

General Financial Modeling Framework

Option Pricing

Valuation of Risk

Modeling Calibration

Interest Rate Market Stock Market


55 J. Schoenmakers (E5)

Topics in Interest Rate Modeling

• Stochastic differential equations → LIBOR Interest rate modeling

• Numerics for stochastic optimal control → Pricing Products

• Inverse problems → Calibration


56 J. Schoenmakers (E5)


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F - Visualization

Algorithmic developments

Statistical models of anatomical shape variability

Model-based auto-segmentation of 3D medical images

3D geometry reconstruction from 2D X-ray images

Optimal shape design in implant/transplant surgery

Industry collaborations

Visage Imaging GmbH / Visualization Sciences Group SAS visualization systems (80k-150k EUR p.a. since 2005)

Implant Manufacturer (undisclosed) CT data segmentation (180k EUR)

Spin-Off 1000shapes GmbH statistical shape modeling and applications

Atlas-based 3D Image Segmentation


58 H.-C. Hege (F2)

www.dzlm.de

German Center for Mathematics Teacher Education

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Integral View

Teac

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Doctoral Studies / BMS Phase II

Studies of Mathematics / BMS Phase I

Secondary School / Berlin Network Schools

Primary School / Profiled Classes in Grades 5/6

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Integral View

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Doctoral Studies / BMS Phase II

Studies of Mathematics / BMS Phase I

Secondary School / Berlin Network Schools

Primary School / Profiled Classes in Grades 5/6

Dezember 2010 April 2011

Initiative of founding a German Center for Mathematics Teacher Education (DZLM) by Deutsche Telekom Stiftung All German universities are invited to submit their concepts for the establishing of a DZLM

July 2011 Success for the concept of the Berlin/NRW-consortium headed by HU Berlin jointly with two other Berlin and three NRW universities

September 2011 Start of the work by the DZLM

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Chronology

Goals

Foundation of the DZLM with the following objectives:

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Development of comprehensive training programs for mathematics educators

In particular, training programs to educate mentor teachers as well as out-of-field teachers

Establishment of nationwide mentor teacher master degree programs

Example of a successful acting center for teacher education in Germany

Concept

Ongoing professionalization of teachers with regard to:

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Mathematics at the interface of content and pedagogical content knowledge

Competence-orientation in mathematics education

Mathematical teaching and learning processes

Educational research

Implementation

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1. Master degree programs for mentor teachers

2. Qualification programs for out-of-field teachers and educators

3. In-service teacher training for all teachers

4. Information and communication platform

Attracting the next generation researchers

Digital „Adventskalender“

(> 12700 participants in 2011)

MATHEatlON 2009, 2010, 2011

„Mathe klingt gut“, 2009

MathFilm-Festival 2008 (> 20 000 DVD’s to schools in Germany)

Year of Mathematics 2008

Rent-the-Center platform

MathInside – Math is everywhere

Highlights

Fotos: Kay Herschelmann


66 DFG Research Center MATHEON

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DFG Research Center MATHEON 67

Participation in (international) High School Competitions

First-Lego-League-Competition 2011

• Since 2011 in cooperation with ESA • Two MATHEON Network Schools: Käthe-Kollwitz-Oberschule & Heinrich-Hertz-Gymnasium • Three MATHEON-Teams in ISS-Finals on 23.01.2012

Thank you for your attention

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