Physics-informed deep learning for digital materials

Abstract

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.

Keywords

• Physics-informed neural networks
• Machine learning
• Finite element analysis
• Digital materials
• Computational mechanics