Name
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. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1109/ICMLA51294.2020.00029 | 2020 19th IEEE International Conference on Machine Learning and Applications (ICMLA) |
Keywords | DocType | ISBN |
Finite difference neural networks,Partial differential equations,Hessian-free trust region method | Conference | 978-1-7281-8471-5 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shi Zheng | 1 | 0 | 0.34 |
| Gulgec Nur Sila | 2 | 0 | 0.34 |
| Albert S. Berahas | 3 | 21 | 4.05 |
| Shamim Pakzad | 4 | 369 | 27.02 |
| Martin Takác | 5 | 752 | 49.49 |