  We formulate extensions to Data Driven 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 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. The present selected numerical tests that establish
the convergence properties of both types of Data Driven solvers and solutions.
