comparison of methods for parametric model order reduction of instationary problems (ii)
DESCRIPTION
held at EU-MORNET Kick-Off MeetingTRANSCRIPT
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
Benchmark Framework
Overview:BenchmarksMethodsTasksTaskmaster
About:Written in MatlabVersion 1.0 will be Open-SourceExtendable with further Benchmarks and MethodsReproducible Results
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)
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
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)
Methods I (About)
Model order reduction codeShould not depend on (or be) propriety code (if possible)(Should be) listed in the MORwiki
Methods II (Interface)
No interface requirements (yet)Must be able to share data with Matlab
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...
Tasks I (About)
Function ContainerEvaluates a set Benchmark,with a set pMOR Method
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
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 (?)...
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
Taskmaster II (Benchmark Ranges)
Currently:Time IntervalFrequency RangeParameter RangeImpulse InputArbitrary Initial ValuesFixed Reduced Dimension
Future:Arbitrary (RMS) InputUncertaintiesVarying Reduced Dimension...
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)‖?
...
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)
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
tl;dl
We have:Basic Benchmark Framework,with Modular Architecture
We need:Tuned MethodsBenchmarks with Integrators
What do you want / need / suggest ?
Thanks!