Projection-tree reduced-order modeling for fast N-body computations
•A new class of reduced order models is presented: projection-tree reduced-order modeling (PTROM).•The method combines tree-algorithms, dimensionality compression, and hyper-reduction.•The PTROM is tested on the N-body fluid-dynamics Biot-Savart law.•Numerical experiments show the PTROM out-performs...
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| Published in: | Journal of computational physics Vol. 459; p. 111141 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cambridge
Elsevier Inc
15.06.2022
Elsevier Science Ltd |
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| ISSN: | 0021-9991, 1090-2716 |
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| Abstract | •A new class of reduced order models is presented: projection-tree reduced-order modeling (PTROM).•The method combines tree-algorithms, dimensionality compression, and hyper-reduction.•The PTROM is tested on the N-body fluid-dynamics Biot-Savart law.•Numerical experiments show the PTROM out-performs classical acceleration techniques.
This work presents a data-driven reduced-order modeling framework to accelerate the computations of nonlocal and N-body methods that model dynamical systems. The proposed framework differs from traditional acceleration methods, like the Barnes–Hut method, which requires online tree building of the state space, or the fast-multipole method, which requires rigorous a priori analysis of governing kernels and online tree building. Our approach combines Barnes–Hut hierarchical decomposition, projection-based reduced-order modeling via the least-squares Petrov–Galerkin (LSPG) projection, and hyper-reduction by way of the Gauss–Newton with approximated tensor (GNAT) approach. The resulting projection-tree reduced-order model (PTROM) enables a drastic reduction in operational count complexity by constructing sparse hyper-reduced pairwise interactions of the non-compact N-body dynamical system. As a result, the presented framework is capable of achieving an operational count complexity that is independent of N, the number of bodies in the numerical domain. Capabilities of the PTROM method are demonstrated on the two-dimensional fluid-dynamic Biot–Savart kernel within a parametric and reproductive setting. Results show the PTROM is capable of achieving over 2000× wall-time speed-up with respect to the full-order model, where the speed-up increases with N. The resulting solution delivers quantities of interest with errors that are less than 0.1% with respect to full-order model. |
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| AbstractList | •A new class of reduced order models is presented: projection-tree reduced-order modeling (PTROM).•The method combines tree-algorithms, dimensionality compression, and hyper-reduction.•The PTROM is tested on the N-body fluid-dynamics Biot-Savart law.•Numerical experiments show the PTROM out-performs classical acceleration techniques.
This work presents a data-driven reduced-order modeling framework to accelerate the computations of nonlocal and N-body methods that model dynamical systems. The proposed framework differs from traditional acceleration methods, like the Barnes–Hut method, which requires online tree building of the state space, or the fast-multipole method, which requires rigorous a priori analysis of governing kernels and online tree building. Our approach combines Barnes–Hut hierarchical decomposition, projection-based reduced-order modeling via the least-squares Petrov–Galerkin (LSPG) projection, and hyper-reduction by way of the Gauss–Newton with approximated tensor (GNAT) approach. The resulting projection-tree reduced-order model (PTROM) enables a drastic reduction in operational count complexity by constructing sparse hyper-reduced pairwise interactions of the non-compact N-body dynamical system. As a result, the presented framework is capable of achieving an operational count complexity that is independent of N, the number of bodies in the numerical domain. Capabilities of the PTROM method are demonstrated on the two-dimensional fluid-dynamic Biot–Savart kernel within a parametric and reproductive setting. Results show the PTROM is capable of achieving over 2000× wall-time speed-up with respect to the full-order model, where the speed-up increases with N. The resulting solution delivers quantities of interest with errors that are less than 0.1% with respect to full-order model. This work presents a data-driven reduced-order modeling framework to accelerate the computations of nonlocal and N-body methods that model dynamical systems. The proposed framework differs from traditional acceleration methods, like the Barnes–Hut method, which requires online tree building of the state space, or the fast-multipole method, which requires rigorous a priori analysis of governing kernels and online tree building. Our approach combines Barnes–Hut hierarchical decomposition, projection-based reduced-order modeling via the least-squares Petrov–Galerkin (LSPG) projection, and hyper-reduction by way of the Gauss–Newton with approximated tensor (GNAT) approach. The resulting projection-tree reduced-order model (PTROM) enables a drastic reduction in operational count complexity by constructing sparse hyper-reduced pairwise interactions of the non-compact N-body dynamical system. As a result, the presented framework is capable of achieving an operational count complexity that is independent of N, the number of bodies in the numerical domain. Capabilities of the PTROM method are demonstrated on the two-dimensional fluid-dynamic Biot–Savart kernel within a parametric and reproductive setting. Results show the PTROM is capable of achieving over 2000× wall-time speed-up with respect to the full-order model, where the speed-up increases with N. The resulting solution delivers quantities of interest with errors that are less than 0.1% with respect to full-order model. |
| ArticleNumber | 111141 |
| Author | Rodriguez, Steven N. Iliopoulos, Athanasios P. Michopoulos, John G. Steuben, John C. Brunton, Steven L. Carlberg, Kevin T. |
| Author_xml | – sequence: 1 givenname: Steven N. surname: Rodriguez fullname: Rodriguez, Steven N. email: steven.rodriguez@nrl.navy.mil organization: Computational Multiphysics Systems Laboratory, U. S. Naval Research Laboratory, Washington DC, United States – sequence: 2 givenname: Athanasios P. surname: Iliopoulos fullname: Iliopoulos, Athanasios P. organization: Computational Multiphysics Systems Laboratory, U. S. Naval Research Laboratory, Washington DC, United States – sequence: 3 givenname: Kevin T. surname: Carlberg fullname: Carlberg, Kevin T. organization: Department of Mechanical Engineering, University of Washington, Seattle, WA, United States – sequence: 4 givenname: Steven L. surname: Brunton fullname: Brunton, Steven L. organization: Department of Mechanical Engineering, University of Washington, Seattle, WA, United States – sequence: 5 givenname: John C. orcidid: 0000-0001-7246-4769 surname: Steuben fullname: Steuben, John C. organization: Computational Multiphysics Systems Laboratory, U. S. Naval Research Laboratory, Washington DC, United States – sequence: 6 givenname: John G. orcidid: 0000-0001-7004-6838 surname: Michopoulos fullname: Michopoulos, John G. organization: Computational Multiphysics Systems Laboratory, U. S. Naval Research Laboratory, Washington DC, United States |
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2 Afkham (10.1016/j.jcp.2022.111141_br0010) 2017; 39 Hansson (10.1016/j.jcp.2022.111141_br0360) 2002; 12 |
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| Snippet | •A new class of reduced order models is presented: projection-tree reduced-order modeling (PTROM).•The method combines tree-algorithms, dimensionality... This work presents a data-driven reduced-order modeling framework to accelerate the computations of nonlocal and N-body methods that model dynamical systems.... |
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| SubjectTerms | Acceleration Barnes–Hut Complexity Computational physics GNAT Hyper-reduction Kernels LSPG Multipoles Projection Reduced order models Reduced-order modeling Reduction Tensors Tree algorithms |
| Title | Projection-tree reduced-order modeling for fast N-body computations |
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