# Sparsely constrained neural networks for model discovery of PDEs

arXiv: https://arxiv.org/abs/2011.04336 · HTML: https://mlsanity.com/paper/2011.04336/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Model discovery in the sparse sampling regime](https://mlsanity.com/paper/2105.00400/) (2021)
- [Fully differentiable model discovery](https://mlsanity.com/paper/2106.04886/) (2021)
- [Sparsistent Model Discovery](https://mlsanity.com/paper/2106.11936/) (2021)

## Abstract (arXiv)

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model discovery to densely sampled data-sets with low noise. Neural network-based approaches circumvent this limit by constructing a surrogate model of the data, but have to date ignored advances in sparse regression algorithms. In this paper we present a modular framework that dynamically determines the sparsity pattern of a deep-learning based surrogate using any sparse regression technique. Using our new approach, we introduce a new constraint on the neural network and show how a different network architecture and sparsity estimator improve model discovery accuracy and convergence on several benchmark examples. Our framework is available at urlhttps://github.com/PhIMaL/DeePyMoD