An attention-based neural ordinary differential equation framework for modeling inelastic processes

TL;DR

This paper introduces an enhanced neural ODE framework incorporating attention mechanisms and convex neural networks to accurately model both conservative and dissipative inelastic behaviors in solid materials.

Contribution

It proposes a novel attention-based internal state flow model with convex neural networks for improved physics-constrained material modeling.

Findings

Accurately models elastic, viscoelastic, and elastoplastic behaviors.

Incorporates attention mechanisms for internal state flow.

Demonstrates effectiveness across multiple material exemplars.

Abstract

To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation (ISV-NODE) framework. In this data-driven, physics-constrained modeling framework internal states are inferred rather than prescribed. The ISV-NODE consists of: (a) a stress model dependent, on observable deformation and inferred internal state, and (b) a model of the evolution of the internal states. The enhancements to ISV-NODE proposed in this work are multifold: (a) a partially input convex neural network stress potential provides polyconvexity in terms of observed strain and inferred state, and (b) an internal state flow model uses common latent features to inform novel attention-based gating and drives the flow of internal state only in dissipative regimes. We demonstrated that this architecture can accurately model dissipative and conservative behavior across an isotropic, isothermal elastic-viscoelastic-elastoplastic spectrum with three exemplars.