# Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning (ME-EQL)

arXiv: https://arxiv.org/abs/2506.08916 · HTML: https://mlsanity.com/paper/2506.08916/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 64 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 10 of 10)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (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)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [A Unified Framework for Sparse Relaxed Regularized Regression: SR3](https://mlsanity.com/paper/1807.05411/) (2018)
- [Sparse Regression: Scalable algorithms and empirical performance](https://mlsanity.com/paper/1902.06547/) (2019)
- [Neural parameter calibration for large-scale multi-agent models](https://mlsanity.com/paper/2209.13565/) (2022)
- [Surrogate Modeling and Control of Medical Digital Twins](https://mlsanity.com/paper/2402.05750/) (2024)

## Abstract (arXiv)

Agent-based modeling (ABM) is a powerful tool for understanding self-organizing biological systems, but it is computationally intensive and often not analytically tractable. Equation learning (EQL) methods can derive continuum models from ABM data, but they typically require extensive simulations for each parameter set, raising concerns about generalizability. In this work, we extend EQL to Multi-experiment equation learning (ME-EQL) by introducing two methods: one-at-a-time ME-EQL (OAT ME-EQL), which learns individual models for each parameter set and connects them via interpolation, and embedded structure ME-EQL (ES ME-EQL), which builds a unified model library across parameters. We demonstrate these methods using a birth--death mean-field model and an on-lattice agent-based model of birth, death, and migration with spatial structure. Our results show that both methods significantly reduce the relative error in recovering parameters from agent-based simulations, with OAT ME-EQL offering better generalizability across parameter space. Our findings highlight the potential of equation learning from multiple experiments to enhance the generalizability and interpretability of learned models for complex biological systems.