Program Synthesis for Simulation-Based Inference: Joint Model Selection and Parameter Estimation

Abstract:Neural simulation-based inference enables parameter estimation for complex models, but typically requires the user to specify a simulator encoding a fixed model structure. We present a framework for joint model selection and parameter estimation that combines large language models for program synthesis with neural simulation-based inference. Given a natural language description of the system and data under investigation, an LLM proposes candidate simulator programs which are iteratively refined via feedback-driven mutation and evaluated using neural density estimation. The approach enables simulation-based inference over a pool of models, not just parameters within a fixed model. On benchmarks spanning deterministic dynamics, stochastic epidemic models, and dark matter substructure inference from gravitational-lensing images, the method identifies plausible model families from open-ended prompts, with accuracy that reflects the information content of the data and identifiability of candidate models.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2607.17540 [cs.LG]

(or arXiv:2607.17540v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.17540 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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