Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world models

Abstract

A primary goal of science is to learn mechanistic world models from limited experimental data, both to explain observations and to predict novel interventions. We introduce the Model Discovery Agent (MDA), which combines LLM proposals for $\mathcal{M}$-open model discovery, experiment design based on Value of Information, and approximate Bayesian inference over model structures, parameters, and stochastic latent trajectories. We apply MDA to learn symbolic reaction rate laws for ChemBench \citep{kabra2026autoscilab}, partially observed ODE models for GlucoseBench \citep{xie2018simglucose,kovatchev2009insilico}, and partially observed SDE models for a new stochastic single-neuron simulator we create. In the appendix, we also show results on various other domains from BoxingGym \citep{gandhi2025boxinggym}. We show that MDA has improved sample efficiency compared to various baseline methods, and the learned models are good predictors but also provide interpretable abstractions of each domain.

arXiv commentv5: Major update: Added GlucoseBench; added experiments with BIC (not just SMC) for marginal likelihood approximation, and de-emphasized SCMC3 narrative; modifed NeuronBench to focus on the stochastic setting; significant rewrite of the main text