# Learning physically consistent mathematical models from data using group sparsity

arXiv: https://arxiv.org/abs/2012.06391 · HTML: https://mlsanity.com/paper/2012.06391/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Discovering PDEs from Multiple Experiments](https://mlsanity.com/paper/2109.11939/) (2021)
- [Fully differentiable model discovery](https://mlsanity.com/paper/2106.04886/) (2021)
- [Sparsistent Model Discovery](https://mlsanity.com/paper/2106.11936/) (2021)
- [Data-driven discovery of multiscale chemical reactions governed by the law of mass action](https://mlsanity.com/paper/2101.06589/) (2021)

## Abstract (arXiv)

We propose a statistical learning framework based on group-sparse regression that can be used to 1) enforce conservation laws, 2) ensure model equivalence, and 3) guarantee symmetries when learning or inferring differential-equation models from measurement data. Directly learning textitinterpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas like biology, high noise levels, sensor-induced correlations, and strong inter-system variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage textitprior knowledge from physical principles to learn "biologically plausible and physically consistent" models rather than models that simply fit the data best. We present a novel group Iterative Hard Thresholding (gIHT) algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing textitpriors in data-driven modeling.