Premium
Data‐driven computing in dynamics
Author(s) -
Kirchdoerfer T.,
Ortiz M.
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5716
Subject(s) - discretization , mathematical optimization , weighting , entropy (arrow of time) , computer science , mathematics , minification , convergence (economics) , algorithm , mathematical analysis , medicine , physics , quantum mechanics , radiology , economics , economic growth
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.