# Discovering PDEs from Multiple Experiments

arXiv: https://arxiv.org/abs/2109.11939 · HTML: https://mlsanity.com/paper/2109.11939/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 15 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 5 of 5)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepMoD: Deep learning for Model Discovery in noisy data](https://mlsanity.com/paper/1904.09406/) (2019)
- [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)
- [Sparsistent Model Discovery](https://mlsanity.com/paper/2106.11936/) (2021)

## Built on by (most cited first, 2 of 2)

- [Integration of knowledge and data in machine learning](https://mlsanity.com/paper/2202.10337/) (2022)
- [Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization](https://mlsanity.com/paper/2606.30699/) (2026)

## Abstract (arXiv)

Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters, initial and boundary conditions that cannot be simply averaged out. We introduce a randomised adaptive group Lasso sparsity estimator to promote grouped sparsity and implement it in a deep learning based PDE discovery framework. It allows to create a learning bias that implies the a priori assumption that all experiments can be explained by the same underlying PDE terms with potentially different coefficients. Our experimental results show more generalizable PDEs can be found from multiple highly noisy datasets, by this grouped sparsity promotion rather than simply performing independent model discoveries.