Data-driven computing in dynamics

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.