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Comparison of Methods for Parametric ModelOrder Reduction of Instationary Problems (II)
Ulrike Baur ([email protected])Peter Benner ([email protected])
Bernard Haasdonk ([email protected])Christian Himpe ([email protected])
Immanuel Martini ([email protected])Mario Ohlberger ([email protected])
EU-MORNET Kick-Off Meeting18.-19.09.2014
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Benchmark Framework
Overview:BenchmarksMethodsTasksTaskmaster
About:Written in MatlabVersion 1.0 will be Open-SourceExtendable with further Benchmarks and MethodsReproducible Results
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Benchmarks I (About)
State-space models
{Ex = (A + Ap)x + Buy = Cx + Du
BYO IntegratorListed in the MORwiki (http://modelreduction.org)
Synthetic (dim(x) = 1000)Microthruster (dim(x) = 4257)Anemometer (dim(x) = 29008)
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Benchmarks II (Interface)
generate-methodAssembles modelOpaque to methodsReturns state-space matrices {A,Ap,B,C ,D,E}
integrate-methodComputes trajectory for given x0, u, pTransparent to methodsReturns fixed-step-width time series
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Benchmarks III (Limitations)
Currently:Single-Input-Single OutputLinear-Time-InvariantSingle Parameter (affinely dependent)Parametrized System Matrix Ap
Future:Multiple-Input-Multiple-OutputLinear-Time-Varying, DDEs, DAEsMany ParametersArbitrary Parametrization {Ap,Bp,Cp,Dp,Ep}Source Term F (Fp)
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Methods I (About)
Model order reduction codeShould not depend on (or be) propriety code (if possible)(Should be) listed in the MORwiki
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Methods II (Interface)
No interface requirements (yet)Must be able to share data with Matlab
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Methods III (On Board)
Currently:PODPOD-GreedyMatrix InterpolationTransfer Function InterpolationPiecewise Tangential H2 InterpolationMulti Parameter Moment MatchingEmpirical (Cross) Gramians
Future:(Variant of) Balanced TruncationLoewner FrameworkInterpolation on Grassmann ManifoldReduced Basis...
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Tasks I (About)
Function ContainerEvaluates a set Benchmark,with a set pMOR Method
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Tasks II (Interface)
{Ar, Apr, Br, Cr, Er, X0r, V, W, Y, Z } =task_METHOD_BENCHMARK(A,Ap,B,C,D,E,X0,U,P,h,T,r)
Gets full order model (A,Ap,B,C,D,E,X0)Input (U)Parameter range (P)Target reduced order (r)Returns reduced order model (Ar,Apr,Br,Cr,Er,X0r)Returns reducing projections (V,W)Can return extra information (Y,Z)for use during the online phase
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Tasks III (Limitations)
Currently:(Benchmark) Input is transparentOnly target reduced orderOwn or benchmark’s integrator
Future:Input will be opaqueTarget offline timeForce own or benchmark’s integrator (?)...
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Taskmaster I (About)
1 Evaluate Full-Order Model2 Execute Offline Phase for all Tasks3 Execute Online Phase for all Tasks
Reduced Order SimulationsError Computation
4 Store Results
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Taskmaster II (Benchmark Ranges)
Currently:Time IntervalFrequency RangeParameter RangeImpulse InputArbitrary Initial ValuesFixed Reduced Dimension
Future:Arbitrary (RMS) InputUncertaintiesVarying Reduced Dimension...
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Taskmaster III (ROM Quality)
Currently:Offline TimeOnline TimeL2-error (in states)L2-error (in outputs)L∞-error (in outputs)H2-error (in outputs)H∞-error (in outputs)Scaled H∞-error (in outputs)ROM Stability Test
Future:Machine independent efficiency indicatorsL1-error (in outputs)maxθ‖y(θ)− yr (θ)‖?
...
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Outlook
Content:More Benchmarks (MORwiki,Oberwolfach,NICONET,Industry,...)
More MethodsNonlinear Systems (ie Gradient Systems)
Architecture:Toolbox Independence (currently: Control System Toolbox)Performance (especially H2 error)Parallelization (per Benchmark)
Usage:Graphical User InterfaceResults Database in MORwiki (possibly versioned)Octave Compatibility (full open-source stack)
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Long Term Goals
Cluster & LocalChoose & Compare different Benchmarks and MethodsExtract Classifications from the MORwikiEvaluate Errors & DurationsEnsure Performance for my new VersionsAll Open-Source & Open-DataTask is sample implementationFullfill Science-Code-Manifesto1
1http://sciencecodemanifesto.org
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tl;dl
We have:Basic Benchmark Framework,with Modular Architecture
We need:Tuned MethodsBenchmarks with Integrators
What do you want / need / suggest ?
Thanks!