On December 15, 2020, I presented the paper of Finite Difference Neural Network: Fast Prediction of Partial Differential Equations at 19TH IEEE International Conference on Machine Learning and Applications.
Video Presentation: Available on Youtube
Co-authors: Dr. Nur Sila Gulgec, Prof. Albert S. Berahas, Prof. Shamim N. Pakzad, and Prof. Martin Takáč
Abstract:
Discovering the underlying behavior of complex systems is an important topic in many science and engineering disciplines. In this paper, we propose a novel neural network framework, finite difference neural networks FD-Net, to learn partial differential equations from data. Specifically, our proposed finite difference inspired network is designed to learn the underlying governing partial differential equations from trajectory data, and to iteratively estimate the future dynamical behavior using only a few trainable parameters. We illustrate the performance (predictive power) of our framework on the heat equation, with and without noise and/or forcing, and compare our results to the Forward Euler method. Moreover, we show the advantages of using a Hessian-Free Trust Region method to train the network.