# SpReME: Sparse Regression for Multi-Environment Dynamic Systems

arXiv: https://arxiv.org/abs/2302.05942 · HTML: https://mlsanity.com/paper/2302.05942/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 12 Feb 2023.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [PredRNN++: Towards A Resolution of the Deep-in-Time Dilemma in Spatiotemporal Predictive Learning](https://mlsanity.com/paper/1804.06300/) (2018)
- [Neural Networks Fail to Learn Periodic Functions and How to Fix It](https://mlsanity.com/paper/2006.08195/) (2020)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Neural ODE Processes](https://mlsanity.com/paper/2103.12413/) (2021)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Disturbance Decoupling for Gradient-based Multi-Agent Learning with Quadratic Costs](https://mlsanity.com/paper/2007.07228/) (2020)

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

- [Position: Biology is the Challenge Physics-Informed ML Needs to Evolve](https://mlsanity.com/paper/2510.25368/) (2025)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)

## Abstract (arXiv)

Learning dynamical systems is a promising avenue for scientific discoveries. However, capturing the governing dynamics in multiple environments still remains a challenge: model-based approaches rely on the fidelity of assumptions made for a single environment, whereas data-driven approaches based on neural networks are often fragile on extrapolating into the future. In this work, we develop a method of sparse regression dubbed SpReME to discover the major dynamics that underlie multiple environments. Specifically, SpReME shares a sparse structure of ordinary differential equation (ODE) across different environments in common while allowing each environment to keep the coefficients of ODE terms independently. We demonstrate that the proposed model captures the correct dynamics from multiple environments over four different dynamic systems with improved prediction performance.