ArXiv

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

2026-07-20 · 04:33 UTC ·Siddharth Mishra-Sharma ·1 min read
Authors
Siddharth Mishra-Sharma
Categories
cs.LG, stat.ML
arXiv
https://arxiv.org/abs/2607.17540v1
PDF
https://arxiv.org/pdf/2607.17540v1

Brief

Mishra-Sharma introduces a simulation-based inference pipeline that combines LLM-driven program synthesis with neural density estimation to perform model selection and parameter estimation jointly, removing the need for a single fixed simulator. Given natural-language problem descriptions, candidate simulators are proposed and mutated with feedback, then scored via neural SBI. Evaluated on deterministic dynamics, epidemic, and gravitational-lensing substructure tasks, the method recovers plausible model families, with performance tied to data information and model identifiability.

Why it matters

The paper (Siddharth Mishra-Sharma, arXiv 2026-07-20) presents a framework that uses large language models to synthesize candidate simulator programs from natural-language descriptions, then iteratively refines them via feedback-driven mutation and evaluates them with neural density estimation to enable joint model selection and parameter estimation.

Key details

  • 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; reported accuracy scales with the information content of the data and the identifiability of candidate models (manuscript: 15+7 pages, 4+2 figures).
Source evidence

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.

Comment: 15+7 pages, 4+2 figures