Recurrent Localization Networks applied to the Lippmann-Schwinger Equation
arXiv:2102.00063 · doi:10.1016/j.commatsci.2021.110356
Abstract
The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e. physics based) or data-driven (i.e. machine-learning based) origins. In order to combine the strengths of these two approaches, we advance a novel machine learning approach for solving equations of the generalized Lippmann-Schwinger (L-S) type. In this paradigm, a given problem is converted into an equivalent L-S equation and solved as an optimization problem, where the optimization procedure is calibrated to the problem at hand. As part of a learning-based loop unrolling, we use a recurrent convolutional neural network to iteratively solve the governing equations for a field of interest. This architecture leverages the generalizability and computational efficiency of machine learning approaches, but also permits a physics-based interpretation. We demonstrate our learning approach on the two-phase elastic localization problem, where it achieves excellent accuracy on the predictions of the local (i.e., voxel-level) elastic strains. Since numerous governing equations can be converted into an equivalent L-S form, the proposed architecture has potential applications across a range of multiscale materials phenomena.
arXiv comment20 pages, 10 figures. Accepted to Computational Materials Science
References in corpus (18)
- Deep Learning in Neural Networks: An Overview
- PyTorch: An Imperative Style, High-Performance Deep Learning Library
- Deep Residual Learning for Image Recognition
- Machine learning and the physical sciences
- A Critical Review of Recurrent Neural Networks for Sequence Learning
- SGDR: Stochastic Gradient Descent with Warm Restarts
- A numerical method for computing the overall response of nonlinear composites with complex microstructure
- Going Deeper with Convolutions
- Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification
- Learned Primal-dual Reconstruction
- Metaheuristic Design of Feedforward Neural Networks: A Review of Two Decades of Research
- A Comprehensive guide to Bayesian Convolutional Neural Network with Variational Inference
- Finite strain FFT-based non-linear solvers made simple
- Recurrent Inference Machines for Solving Inverse Problems
- Perspective: Inverse methods for material design
- Materials knowledge system for nonlinear composites
- Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation
- A multiscale strategy for Bayesian inference using transport maps