A learning-based multiscale method and its application to inelastic impact problems

TL;DR

This paper introduces a multiscale modeling approach that uses deep neural networks to efficiently and accurately simulate inelastic impact problems, specifically applied to magnesium, without requiring prior detailed knowledge of fine-scale behavior.

Contribution

It presents a novel learning-based multiscale method that combines neural networks with model reduction to directly incorporate fine-scale behavior into coarse-scale impact simulations.

Findings

High-fidelity neural network approximation of fine-scale behavior

Reduced computational cost in multiscale impact simulations

Successful application to magnesium impact problems

Abstract

The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale modeling seeks to understand these interactions by exploiting the inherent hierarchy where the behavior at a coarser scale regulates and averages the behavior at a finer scale. This requires the repeated solution of computationally expensive finer-scale models, and often a priori knowledge of those aspects of the finer-scale behavior that affect the coarser scale (order parameters, state variables, descriptors, etc.). We address this challenge in a two-scale setting where we learn the fine-scale behavior from off-line calculations and then use the learnt behavior directly in coarse scale calculations. The approach draws from recent successes of deep neural networks, in combination with ideas from model reduction. The approach builds on the recent success of deep neural networks by combining their approximation power in high dimensions with ideas from model reduction. It results in a neural network approximation that has high fidelity, is computationally inexpensive, is independent of the need for a priori knowledge, and can be used directly in the coarse scale calculations. We demonstrate the approach on problems involving the impact of magnesium, a promising light-weight structural and protective material.