FD-Net with Auxiliary Time Steps: Fast Prediction of PDEs using Hessian-Free Trust-Region Methods
arXiv:1910.12680
Abstract
Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn hidden partial differential equations from given data and iteratively estimate future dynamical behavior. The methodology designs the filter sizes such that they mimic the finite difference between the neighboring points. By learning the governing equation, the network predicts the future evolution of the solution by using only a few trainable parameters. In this paper, we provide numerical results to compare the efficiency of the second-order Trust-Region Conjugate Gradient (TRCG) method with the first-order ADAM optimizer.
arXiv commentPaper accepted to NeurIPS workshop
References in corpus (6)
- Adam: A Method for Stochastic Optimization
- Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
- Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
- Neural Ordinary Differential Equations
- PDE-Net: Learning PDEs from Data
- Deep Learning the Physics of Transport Phenomena