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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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 384; p. 113973
Main Authors: Rizzi, Francesco, Parish, Eric J., Blonigan, Patrick J., Tencer, John
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.10.2021
Elsevier BV
Elsevier
Subjects:
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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Summary: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.
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AC04-94AL85000; NA0003525
SAND-2021-6660J
USDOE National Nuclear Security Administration (NNSA)
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.113973