# Data-Driven Computing in Dynamics

## TL;DR

This paper extends Data Driven Computing methods to include time integration, introducing schemes that assign data relevance dynamically and demonstrate convergence through numerical tests.

## Contribution

It develops new time-integrated Data Driven Computing schemes with variable data relevance and maximum-entropy weighting, expanding previous static equilibrium approaches.

## Key findings

- Schemes incorporate time integration and relevance weighting.
- Numerical tests confirm convergence properties.
- Methods handle dynamic systems with phase space constraints.

## Abstract

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.