Program Synthesis for Simulation-Based Inference: Joint Model Selection and Parameter Estimation
2026-07-20 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a method that uses large language models to create and improve computer programs simulating real-world systems based on simple descriptions. These programs represent different possible explanations (models) for observed data. Their approach combines this with neural methods to estimate which models and parameters best fit the data. This lets them not only fine-tune model details but also choose between different model types. They tested this on tasks like disease spread and cosmic phenomena, where the method successfully found suitable models depending on the data.
neural simulation-based inferencelarge language modelsprogram synthesismodel selectionparameter estimationneural density estimationdeterministic dynamicsstochastic epidemic modelsgravitational lensingdark matter substructure
Authors
Siddharth Mishra-Sharma
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.