Data-Driven Games in Computational Mechanics
Kerstin Weinberg Laurent Strainier Sergio Conti Michael Ortiz
We resort to game theory in order to formulate Data-Driven methods for solid
mechanics in which stress and strain players pursue different objectives. The
objective of the stress player is to minimize the discrepancy to a material
data set, whereas the objective of the strain player is to ensure the
admissibility of the mechanical state, in the sense of compatibility and
equilibrium. We show that, unlike the cooperative Data-Driven games proposed in
the past, the new non-cooperative Data-Driven games identify an effective
material law from the data and reduce to conventional displacement
boundary-value problems, which facilitates their practical implementation.
However, unlike supervised machine learning methods, the proposed
non-cooperative Data-Driven games are unsupervised, ansatz-free and
parameter-free. In particular, the effective material law is learned from the
data directly, without recourse to regression to a parameterized class of
functions such as neural networks. We present analysis that elucidates
sufficient conditions for convergence of the Data-Driven solutions with respect
to the data. We also present selected examples of implementation and
application that demonstrate the range and versatility of the approach.