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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Bibliographic Details
Published inInternational journal for numerical methods in engineering Vol. 113; no. 11; pp. 1697 - 1710
Main Authors Kirchdoerfer, T., Ortiz, M.
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 16.03.2018
Subjects
Data points
data science
dynamics
Energy conservation
Entropy of solution
Formulations
Free energy
model‐free computing
noisy data
Optimization
Solvers
Static equilibrium
Time integration
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ISSN0029-5981
1097-0207
DOI10.1002/nme.5716

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Summary: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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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5716