A generalized physics-driven neural network for micromechanical and microstructural evolution of heterogeneous materials

Physics-driven neural networks (PDNNs) have shown great promise for micromechanical applications, but are currently facing challenges in terms of generalization for tackling time-dependent problems of inhomogeneous materials. Here we present a generalized PDNN (GPDNN) framework for micromechanical and microstructural evolution by incorporating the Fourier feature layer, multi-output scheme, and self-adaptive learning weighting. This GPDNN retains the advantages of PDNN, i.e., utilizing unlabeled data and avoiding unphysical behavior, and formulates both strong form and weak form based loss functions. The generality and accuracy of GPDNN are then demonstrated across various time-dependent problems, including Eshelby's inclusion problem, elastodynamics of porous and polycrystalline materials, and microstructure evolution governed by phase-field equations. The effect of multi-output scheme and self-adaptive learning weighting, the key enablers of performance improvement for GPDNN, are further analyzed, together with computational efficiency comparison between GPDNN and other methods. It is shown that GPDNN achieves higher efficiency and accuracy as compared to PDNN in solving multiscale dynamical problems, highlighting the proposed GPDNN framework as a more generalized tool for addressing critical challenges in computational micromechanics and materials science.