# Data Driven Computing with Noisy Material Data Sets

## TL;DR

This paper introduces max-ent Data Driven Computing, a robust framework that uses clustering and maximum-entropy principles to handle noisy material data sets, improving convergence and outlier resistance.

## Contribution

It generalizes existing Data Driven Computing by incorporating maximum-entropy estimation for robustness against outliers and noise.

## Key findings

- The scheme converges reliably in numerical tests.
- Max-ent approach outperforms traditional methods with noisy data.
- Distance-minimizing schemes are recovered at zero temperature.

## Abstract

We formulate a Data Driven Computing paradigm, termed max-ent Data Driven Computing, that generalizes distance-minimizing Data Driven Computing and is robust with respect to outliers. Robustness is achieved by means of clustering analysis. Specifically, we assign data points a variable relevance depending on distance to the solution and on maximum-entropy estimation. The resulting scheme consists of the minimization of a suitably-defined free energy over phase space subject to compatibility and equilibrium constraints. Distance-minimizing Data Driven schemes are recovered in the limit of zero temperature. We present selected numerical tests that establish the convergence properties of the max-ent Data Driven solvers and solutions.