# Sparsistent Model Discovery

arXiv: https://arxiv.org/abs/2106.11936 · HTML: https://mlsanity.com/paper/2106.11936/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [DeepMoD: Deep learning for Model Discovery in noisy data](https://mlsanity.com/paper/1904.09406/) (2019)
- [Robust discovery of partial differential equations in complex situations](https://mlsanity.com/paper/2106.00008/) (2021)
- [Stability selection enables robust learning of partial differential equations from limited noisy data](https://mlsanity.com/paper/1907.07810/) (2019)
- [Learning physically consistent mathematical models from data using group sparsity](https://mlsanity.com/paper/2012.06391/) (2020)
- [Machine Discovery of Partial Differential Equations from Spatiotemporal Data](https://mlsanity.com/paper/1909.06730/) (2019)
- [Sparsely constrained neural networks for model discovery of PDEs](https://mlsanity.com/paper/2011.04336/) (2020)
- [Model discovery in the sparse sampling regime](https://mlsanity.com/paper/2105.00400/) (2021)

## Built on by (most cited first, 1 of 1)

- [Discovering PDEs from Multiple Experiments](https://mlsanity.com/paper/2109.11939/) (2021)

## Abstract (arXiv)

Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model discovery algorithms based on sparse regression can actually recover the underlying physical processes. In this work, we show the design matrices used to infer the equations by sparse regression can violate the irrepresentability condition (IRC) of the Lasso, even when derived from analytical PDE solutions (i.e. without additional noise). Sparse regression techniques which can recover the true underlying model under violated IRC conditions are therefore required, leading to the introduction of the randomised adaptive Lasso. We show once the latter is integrated within the deep learning model discovery framework DeepMod, a wide variety of nonlinear and chaotic canonical PDEs can be recovered: (1) up to O(2) higher noise-to-sample ratios than state-of-the-art algorithms, (2) with a single set of hyperparameters, which paves the road towards truly automated model discovery.