# Principled model selection for stochastic dynamics

arXiv: https://arxiv.org/abs/2501.10339 · HTML: https://mlsanity.com/paper/2501.10339/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 45 references that are in the map.
- First posted on arXiv 17 Jan 2025.

## Builds on (most cited first, 8 of 8)

- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [A Review of Data-Driven Discovery for Dynamic Systems](https://mlsanity.com/paper/2210.10663/) (2022)
- [Approximate Bayes learning of stochastic differential equations](https://mlsanity.com/paper/1702.05390/) (2017)
- [Discovering stochastic partial differential equations from limited data using variational Bayes inference](https://mlsanity.com/paper/2306.15873/) (2023)
- [Discovering stochastic dynamical equations from biological time series data](https://mlsanity.com/paper/2205.02645/) (2022)

## Abstract (arXiv)

Complex dynamical systems, from macromolecules to ecosystems, are often modeled by stochastic differential equations. To learn such models from data, a common approach involves sparse selection among a large function library. However, we show that overfitting arises not just from individual model complexity, but also from the combinatorial growth of possible models. To address this, we introduce Parsimonious Stochastic Inference (PASTIS), a principled method combining likelihood-estimation statistics with extreme value theory to suppress superfluous parameters. PASTIS outperforms existing methods and reliably identifies minimal models, even with low sampling rates or measurement error. It extends to stochastic partial differential equations, and applies to ecological networks and reaction-diffusion dynamics.