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

• URL: http://arxiv.org/abs/2607.17540v1
• Date: Mon, 20 Jul 2026 04:33:35 GMT
• Title: Program Synthesis for Simulation-Based Inference: Joint Model Selection and Parameter Estimation
• Abstract summary: We present a framework for joint model selection and parameter estimation that combines large language models for program synthesis with neural simulation-based inference.<n>The approach enables simulation-based inference over a pool of models, not just parameters within a fixed model.
• Score: 0.038073142980733
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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