Data‐driven computing in dynamics
Summary We formulate extensions to data‐riven computing for both distance‐minimizing and entropy‐maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here, formulations assign data points to...
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| Veröffentlicht in: | International journal for numerical methods in engineering Jg. 113; H. 11; S. 1697 - 1710 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Bognor Regis
Wiley Subscription Services, Inc
16.03.2018
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | Summary
We formulate extensions to data‐riven computing for both distance‐minimizing and entropy‐maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here, formulations assign data points to a variable relevance depending on distance to the solution and on maximum‐entropy weighting, with distance‐minimizing schemes discussed as a special case. The resulting schemes consist of the minimization of a suitably defined free energy over phase space subject to compatibility and a time‐discretized momentum conservation constraint. We present selected numerical tests that establish the convergence properties of both types of data‐driven solvers and solutions. |
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| AbstractList | We formulate extensions to data‐riven computing for both distance‐minimizing and entropy‐maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here, formulations assign data points to a variable relevance depending on distance to the solution and on maximum‐entropy weighting, with distance‐minimizing schemes discussed as a special case. The resulting schemes consist of the minimization of a suitably defined free energy over phase space subject to compatibility and a time‐discretized momentum conservation constraint. We present selected numerical tests that establish the convergence properties of both types of data‐driven solvers and solutions. Summary We formulate extensions to data-riven computing for both distance-minimizing and entropy-maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here, formulations assign data points to a variable relevance depending on distance to the solution and on maximum-entropy weighting, with distance-minimizing schemes discussed as a special case. The resulting schemes consist of the minimization of a suitably defined free energy over phase space subject to compatibility and a time-discretized momentum conservation constraint. We present selected numerical tests that establish the convergence properties of both types of data-driven solvers and solutions. Summary We formulate extensions to data‐riven computing for both distance‐minimizing and entropy‐maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here, formulations assign data points to a variable relevance depending on distance to the solution and on maximum‐entropy weighting, with distance‐minimizing schemes discussed as a special case. The resulting schemes consist of the minimization of a suitably defined free energy over phase space subject to compatibility and a time‐discretized momentum conservation constraint. We present selected numerical tests that establish the convergence properties of both types of data‐driven solvers and solutions. |
| Author | Kirchdoerfer, T. Ortiz, M. |
| Author_xml | – sequence: 1 givenname: T. surname: Kirchdoerfer fullname: Kirchdoerfer, T. organization: California Institute of Technology, Graduate Aerospace Laboratories – sequence: 2 givenname: M. orcidid: 0000-0001-5877-4824 surname: Ortiz fullname: Ortiz, M. email: ortiz@aero.caltech.edu organization: California Institute of Technology, Graduate Aerospace Laboratories |
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We formulate extensions to data‐riven computing for both distance‐minimizing and entropy‐maximizing schemes to incorporate time integration. Previous... We formulate extensions to data‐riven computing for both distance‐minimizing and entropy‐maximizing schemes to incorporate time integration. Previous works... Summary We formulate extensions to data-riven computing for both distance-minimizing and entropy-maximizing schemes to incorporate time integration. Previous... |
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| SubjectTerms | Data points data science dynamics Energy conservation Entropy of solution Formulations Free energy model‐free computing noisy data Optimization Solvers Static equilibrium Time integration |
| Title | Data‐driven computing in dynamics |
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