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

TL;DR

This paper introduces multi-experiment equation learning (ME-EQL), extending traditional EQL to improve model generalizability across parameter spaces in agent-based models of biological systems.

Contribution

The paper proposes two novel ME-EQL methods, OAT ME-EQL and ES ME-EQL, to learn models across multiple parameters, enhancing generalizability and reducing errors in complex biological simulations.

Findings

Both methods reduce error in parameter recovery.

OAT ME-EQL offers superior generalizability.

Methods demonstrated on biological models.

Abstract

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.