  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.
