Revealing the Predictive Power of Neural Operators for Strain Evolution in Digital Composites

TL;DR

This paper demonstrates that Neural Operators, especially Fourier NO, can efficiently and accurately predict strain evolution in digital composites, significantly reducing computational costs compared to traditional methods.

Contribution

The study introduces the use of Neural Operators for predicting strain evolution in composites, highlighting Fourier NO's super-resolution and generalization capabilities with high efficiency.

Findings

Neural Operators accurately predict multiple future strain states from initial frames.

Fourier NO outperforms Wavelet and Multi-wavelet NOs in accuracy and speed.

FNO reduces inference time by nearly three orders of magnitude compared to finite element methods.

Abstract

The demand for high-performance materials, along with advanced synthesis technologies such as additive manufacturing and 3D printing, has spurred the development of hierarchical composites with superior properties. However, computational modelling of such composites using physics-based solvers, while enabling the discovery of optimal microstructures, have prohibitively high computational cost hindering their practical application. To this extent, we show that Neural Operators (NOs) can be used to learn and predict the strain evolution in 2D digital composites. Specifically, we consider three architectures, namely, Fourier NO (FNO), Wavelet NO (WNO), and Multi-wavelet NO (MWT). We demonstrate that by providing a few initial strain frames as input, NOs can accurately predict multiple future time steps in an extremely data-efficient fashion, especially WNO. Further, once trained, NOs forecast the strain trajectories for completely unseen boundary conditions. Among NOs, only FNO offers super-resolution capabilities for estimating strains at multiple length scales, which can provide higher material and pixel-wise resolution. We also show that NOs can generalize to arbitrary geometries with finer domain resolution without the need for additional training. Based on all the results presented, we note that the FNO exhibits the best performance among the NOs, while also giving minimum inference time that is almost three orders magnitude lower than the conventional finite element solutions. Thus, FNOs can be used as a surrogate for accelerated simulation of the strain evolution in complex microstructures toward designing the next composite materials.