Explainable artificial intelligence for mechanics: physics-informing neural networks for constitutive models

TL;DR

This paper introduces a novel explainable AI approach for mechanics, using post hoc analysis of neural networks trained on mechanical data to reveal their internal representations and relate them to known physical functions.

Contribution

It proposes a physics-informing method that explains neural network parameters after training, bridging the gap between black-box models and mechanical interpretability.

Findings

PCA decorrelates neural network representations, aiding interpretation.

Systematic hyperparameter search improves neural network architecture selection.

Case studies suggest the approach can identify analytical solutions for material modeling.

Abstract

(Artificial) neural networks have become increasingly popular in mechanics to accelerate computations with model order reduction techniques and as universal models for a wide variety of materials. However, the major disadvantage of neural networks remains: their numerous parameters are challenging to interpret and explain. Thus, neural networks are often labeled as black boxes, and their results often elude human interpretation. In mechanics, the new and active field of physics-informed neural networks attempts to mitigate this disadvantage by designing deep neural networks on the basis of mechanical knowledge. By using this a priori knowledge, deeper and more complex neural networks became feasible, since the mechanical assumptions could be explained. However, the internal reasoning and explanation of neural network parameters remain mysterious. Complementary to the physics-informed approach, we propose a first step towards a physics-informing approach, which explains neural networks trained on mechanical data a posteriori. This novel explainable artificial intelligence approach aims at elucidating the black box of neural networks and their high-dimensional representations. Therein, the principal component analysis decorrelates the distributed representations in cell states of RNNs and allows the comparison to known and fundamental functions. The novel approach is supported by a systematic hyperparameter search strategy that identifies the best neural network architectures and training parameters. The findings of three case studies on fundamental constitutive models (hyperelasticity, elastoplasticity, and viscoelasticity) imply that the proposed strategy can help identify numerical and analytical closed-form solutions to characterize new materials.