Data-Driven Games in Computational Mechanics
This work addresses the challenge of unsupervised, ansatz-free material modeling in computational mechanics for engineers and researchers, offering a novel alternative to supervised methods, though it builds incrementally on prior cooperative game formulations.
The paper tackles the problem of formulating Data-Driven methods for solid mechanics by using non-cooperative game theory, where stress and strain players have different objectives, resulting in an effective material law learned directly from data without parameterization. It shows that this approach reduces to conventional boundary-value problems, facilitating practical implementation, with analysis on convergence conditions and examples demonstrating versatility.
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.