Papers › NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling...
NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data
Yifan Sun, Linan Zhang, Hayden Schaeffer
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing system which respects the intrinsic differential structure. The unknown governing model is parameterized by using both (shallow) multilayer perceptrons and nonlinear differential terms, in order to incorporate relevant correlations between spatio-temporal samples. We demonstrate the approach on several examples where the data is sampled from various dynamical systems and give a comparison to recurrent networks and other data-discovery methods. In addition, we show that for MNIST and Fashion MNIST, our approach lowers the parameter cost as compared to other deep neural networks.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Image Classification | Fashion-MNIST | NeuPDE | Percentage error | 7.6 | #12 of 34 | Archive leaderboard | report |
| Image Classification | MNIST | NeuPDE | Percentage error | 0.51 | #38 of 81 | Archive leaderboard | report |
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