Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning for biological systems

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: (i) one-at-a-time ME-EQL (OAT ME-EQL), which learns individual models for each parameter set and connects them via interpolation, and (ii) embedded structure ME-EQL (ES ME-EQL), which builds a unified model library across parameters. We demonstrate these methods by learning continuum models from a noisy birth–death mean-field model and from an on-lattice agent-based model of birth, death, and migration with spatial structure, often used to investigate cell biology experiments. We 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.Author summary: Biological systems often display complex patterns and dynamics across space and time in response to interactions between individual units, such as cells, molecules, or animals. Mathematical modeling is an essential tool to understand how biological interactions scale into emergent behaviors. Agent-based models are an especially powerful framework for investigating relevant biological mechanisms by simulating interactions between agents. A limitation of these models, however, is their computationally intensive nature and the large number of input parameters. These challenges hinder modelers’ ability to connect agent-based models to biological data for data-driven tasks such as parameter inference, which requires numerous model simulations. Here, we propose novel extensions of sparse regression techniques for equation learning, aimed at learning parameterized differential equations from multiple agent-based model experiments. Our methods derive differential equations that describe the population dynamics across parameter regimes, which we demonstrate using a spatial birth–death–migration model commonly applied to cell biology experiments. We find that these data-driven methods learn equations that generalize across parameter space and also significantly improve the recovery of parameters from agent-based model datasets.