Physics-informed deep learning for digital materials

In this work, a physics-informed neural network (PINN) designed specifically for analyzing digital materials is introduced. This proposed machine learning (ML) model can be trained free of ground truth data by adopting the minimum energy criteria as its loss function. Results show that our energy-based PINN reaches similar accuracy as supervised ML models. Adding a hinge loss on the Jacobian can constrain the model to avoid erroneous deformation gradient caused by the nonlinear logarithmic strain. Lastly, we discuss how the strain energy of each material element at each numerical integration point can be calculated parallelly on a GPU. The algorithm is tested on different mesh densities to evaluate its computational efficiency which scales linearly with respect to the number of nodes in the system. This work provides a foundation for encoding physical behaviors of digital materials directly into neural networks, enabling label-free learning for the design of next-generation composites. (C) 2021 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics.

Automated summary

A physics-informed neural network (PINN) for digital materials analysis is introduced, trained without ground truth data using minimum energy criteria. The model reached similar accuracy as supervised ML models and prevented erroneous deformation gradients with hinge loss on the Jacobian. Parallel computing on GPU for strain energy calculation showed linear scalability with the number of nodes, laying the foundation for label-free learning in designing next-generation composites.