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Learning Process-Based Models of Dynamic Systems
Nikola SimidjievskiJozef Stefan Institute, Slovenia
HIPEAC 2014 LJUBLJANA
Introduction• Equation Discovery (ED) is a subfield of machine learning, dealing with the task of inducing scientific laws and models in form of equations from observations.
• In the context of modeling system dynamics, the observations are time-series and the models take form of ordinary differential equations (ODEs)
• Process-Based Modeling (PBM) is an ED approach, which integrates domain-specific modeling knowledge and data into explanatory models of the observed systems.
• Using modeling knowledge formulated in a library, and observed data from the system at hand, this approach induces process-based models - an accurate, understandable and modular representation of the observed system dynamics.
Process-based models• Conceptual (high-level) representation of system dynamics.
• Process-based models are comprised of entities and processes.
• Entities and processes represent specific components and interactions observed in the system.
• Entities represent the state/variable of the system.
• Processes the represent the interactions between the entities.
• Knowledge is represented as library of entity and process templates.
The task of learning process-based models • Determining the structure of the model (ODE) Heuristic/exhaustive search over the space of suitable
candidate models • Parameter estimation finding values which minimize the difference (error)
between simulated and measured (real) data
• 3 Inputs : Library (Domain specific)
Conceptual model (Problem specific)
Data (Task specific)
Process-Based Library
Nataša Atanasova et al. , Constructing a library of domain knowledge for automated modelling of aquatic ecosystems, Ecological Modelling, 2006
Library of domain-specific modeling knowledge
ProBMoT (Čerepnalkoski, Simidjievski, Tanevski et al.)
ProBMoT1 (Process Based Modeling Tool) Tool for complete modeling, parameter estimation and simulation of process-based models
Darko Čerepnalkoski et al., The influence of parameter fitting methods on model structure selection in automated modeling of aquatic ecosystems, EM 2012
The Process
Parameter Estimation
Model generator
Library
Measurements
ConceptualModel
Specific models structures
The Process
Parameter Estimation
~50K-100KSimulations
per Structure
Parameter Estimation
Model generator
Library
Measurements
ConceptualModel
Specific models structures
Error values
Best Model
The Process
Parameter Estimation Parameter Estimation
Model generator
Library
Measurements
ConceptualModel
Validation
The Process Job
Best Model
Parameter Estimation Parameter Estimation
Measurements
Model generator
ConceptualModel
Library
Validation
Improved predictive performanceBetter address the complexity of real systems: combination of base models for better description of observed behavior
Training setT
T1
T2
TN
Model M1
Model M2
Model MN
Learningalgorithm
Learningalgorithm
Learningalgorithm
Ensemble
Ensembles
Ensembles of Process-based models•Base models are homogeneous
•Training data is represented as a time series.
•Each base model is trained on different samples of the data (Bagging)
•2-D space of candidate models A list of base models is generated by every ensemble iteration / replica
Parameter Estimation
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Sample ofMeasurements
Parameter Estimation
Model generator
ConceptualModel
Library
Sample ofMeasurements
Best Model 1 Best Model 2 Best Model 100
Parameter Estimation
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Let say 100
Sample ofMeasurements
Parameter Estimation
Model generator
ConceptualModel
Library
Sample ofMeasurements
Validation
Parameter Estimation
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Sample ofMeasurements
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Model generator
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Sample ofMeasurements
Job
The “fun” stuff…
& (executable ="run_[JOB]##.sh") (jobname = "Awsome_[JOB]##") (stdout = "[JOB]##.out") (stderr = "[JOB]##.err") (inputfiles = ("[JOB]##.tar") (outputfiles = ("[JOB]##.tgz") (cputime = "30 days") (memory = "2560") #!/bin/bash
tar -xf [JOB]##.tar cd JOB_workingDir java -Xms256m -Xmx2048m -jar PROBMOT.jar task/PROBMO_TaskSpec.xml
cd .. tar czf [JOB]##/out/ [JOB]##/*.log
.xRSL
run_[JOB]##.sh
Case Study : Population Dynamics in Lake Ecosystem
Modeling phytoplankton dynamics in lake ecosystems (1 ODE)
Lake Bled (Slovenia)
Lake Kasumigaura (Japan)
Lake Zurich (Switzerland) Lake Walensee (Switzerland)
Experiments Experimental Size 100 Ensemble Iterations 4 Different Lake Domains (Lake Bled, Lake Kasumigaura, Lake
Zurich, Lake Walensee) Total of 40 different modeling scenarios ~200 Model Structures per scenario 50000 Iterations in the Parameter Estimation Phase per
structure 1 Model (Structure Identification + Parameter
Estimation) = 2-3 minutes
=> Total Time of the whole experiment ~ 1,000,000min or ~ 2 years
We did it in ….. 3 Days
Nikola Simidjievski et al., Learning ensembles of population dynamics models and their application to modelling aquatic ecosystems., EM 2014
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