Finite difference neural networks: Fast prediction of partial differential equations

Image credit: FD-Net


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.

IEEE International Conference on Machine Learning and Applications
Zheng Shi
Zheng Shi
Team Lead, Data Science | Ph.D., Machine Learning & Optimization

Deep Learning, Machine Learning, Optimization Algorithms, and Data Science.