A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels...

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Vydané v:	Computer methods in applied mechanics and engineering Ročník 384; s. 113973
Hlavní autori:	Rizzi, Francesco, Parish, Eric J., Blonigan, Patrick J., Tencer, John
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.10.2021 Elsevier BV Elsevier
Predmet:	BLAS C++ C++ Performance portability compute-bound Compute-bound kernels Dynamical systems Elastic seismic shear waves elastic shear waves Galerkin Galerkin method generic programming GPU HPC Invariants Kokkos Linear time-invariant dynamical systems many-core Mathematical analysis MATHEMATICS AND COMPUTING memory bandwidth bound Model accuracy Model reduction Monte Carlo POD Projection-based model reduction Reduced order models S waves seismic modeling Tensors Uncertainty quantification Uncertainty quantification C++ Performance portability Compute-bound kernels Linear time-invariant dynamical systems Projection-based model reduction Elastic seismic shear waves
ISSN:	0045-7825, 1879-2138
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Popis
Shrnutí:	This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. Finally, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field. •ROMs for linear time-invariant dynamical systems are memory bandwidth bound•Compute-bound ROM formulations benefit many-query problems.•Compute-bound ROM formulations are suited for modern many-core architectures.•Uncertainty quantification for elastic shear waves simulations can benefit from ROMs.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 AC04-94AL85000; NA0003525 SAND-2021-6660J USDOE National Nuclear Security Administration (NNSA)
ISSN:	0045-7825 1879-2138
DOI:	10.1016/j.cma.2021.113973