A Probabilistic Framework for LLM-Based Model Discovery
This work addresses the challenge of automating scientific model discovery for researchers, offering a probabilistic framework that unifies proposal, refinement, and selection, though it is incremental as it builds on existing LLM-based approaches.
The paper tackles the problem of discovering mechanistic simulator models from observational data by recasting model discovery as probabilistic inference, introducing ModelSMC based on Sequential Monte Carlo sampling, which improves posterior predictive checks and yields interpretable mechanisms in experiments on real-world scientific systems.
Automated methods for discovering mechanistic simulator models from observational data offer a promising path toward accelerating scientific progress. Such methods often take the form of agentic-style iterative workflows that repeatedly propose and revise candidate models by imitating human discovery processes. However, existing LLM-based approaches typically implement such workflows via hand-crafted heuristic procedures, without an explicit probabilistic formulation. We recast model discovery as probabilistic inference, i.e., as sampling from an unknown distribution over mechanistic models capable of explaining the data. This perspective provides a unified way to reason about model proposal, refinement, and selection within a single inference framework. As a concrete instantiation of this view, we introduce ModelSMC, an algorithm based on Sequential Monte Carlo sampling. ModelSMC represents candidate models as particles which are iteratively proposed and refined by an LLM, and weighted using likelihood-based criteria. Experiments on real-world scientific systems illustrate that this formulation discovers models with interpretable mechanisms and improves posterior predictive checks. More broadly, this perspective provides a probabilistic lens for understanding and developing LLM-based approaches to model discovery.