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G-Sim: Generative Simulations with Large Language Models and Gradient-Free Calibration
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G-Sim uses an LLM in an iterative loop to propose simulator structure and gradient-free optimization or simulation-based inference to calibrate parameters, outperforming data-driven and LLM-only baselines on three simulation tasks.
Problem
Building robust simulators for "what if" system-level experiments is costly; purely data-driven world models fail out-of-distribution and purely LLM-generated simulators lack empirical calibration, especially with fragmented, stochastic, or discrete components.
Approach
A hybrid loop where an LLM proposes simulator structure (submodules and couplings) from domain knowledge, parameters are calibrated with likelihood-free, gradient-free methods (evolutionary strategies or neural posterior estimation), and diagnostics feed textual feedback back to the LLM for structural refinement.
Key results
- G-Sim-SBI reports the lowest test Wasserstein distance on all three tasks, e.g. 0.351 on COVID-19 vs 3.30 for the best data-driven Transformer.
- On Hospital Beds, G-Sim-SBI reaches 5.24 Wasserstein versus about 199 for data-driven baselines.
- In policy optimization on Hospital Bed Scheduling, the G-Sim-selected policy (tau=15, delta B=2500, cost 32,703) is close to the ground-truth optimum (tau=10, cost 29,274).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Combine LLM-guided structural design with SBI calibration | G-Sim on COVID-19 · COVID-19 | Wasserstein distance: 3.30±0.15 -> 0.351±0.094 | Helped |
| Combine LLM-guided structural design with SBI calibration | G-Sim on Supply Chain · Supply Chain | Wasserstein distance: 2.29±0.06 -> 1.22±1.68 | Helped |
| Combine LLM-guided structural design with SBI calibration | G-Sim on Hospital Beds · Hospital Beds | Wasserstein distance: 199±0.25 -> 5.24±2.70 | Helped |
| Add parameter calibration and iterative structural refinement instead of generating code once without calibration (ablation) | G-Sim-ES on COVID-19 · COVID-19 | Wasserstein distance: 1.17±0.71 -> 0.405±0.060 | Helped |
| Add parameter calibration and iterative structural refinement instead of generating code once without calibration (ablation) | G-Sim-ES on Supply Chain · Supply Chain | Wasserstein distance: 2.63±2.79 -> 1.55±1.39 | Mixed |
| Add parameter calibration and iterative structural refinement instead of generating code once without calibration (ablation) | G-Sim-ES on Hospital Beds · Hospital Beds | Wasserstein distance: 102±1.01 -> 101±17.4 | Helped |
| Add structural design adjustment to numerical-parameter-only optimization (ablation) | G-Sim-ES on COVID-19 · COVID-19 | Wasserstein distance: 0.469±0.107 -> 0.405±0.060 | Hurt |
| Add structural design adjustment to numerical-parameter-only optimization (ablation) | G-Sim-ES on Supply Chain · Supply Chain | Wasserstein distance: 9.89±15.3 -> 1.55±1.39 | Mixed |
| Add structural design adjustment to numerical-parameter-only optimization (ablation) | G-Sim-ES on Hospital Beds · Hospital Beds | Wasserstein distance: 103±2.06 -> 101±17.4 | Helped |
Surprising findings
- G-Sim-ES zero-shot ablation without iterative refinement is already competitive on COVID-19 (1.17) and Supply Chain (2.63), showing the LLM's initial structure carries much of the performance.
Limitations
- SBI guarantees assume correct model structure, so posteriors do not capture structural uncertainty.
- Scalability to extremely high-dimensional systems is a stated limitation.
- Structural identifiability may leave multiple structures equally consistent with data.
Experimental setup
Datasets: COVID-19 SIR simulation trajectories Supply Chain beer game trajectories Hospital Bed Scheduling trajectories
Benchmarks: COVID-19 SIR Supply Chain Hospital Bed Scheduling
Metrics: Wasserstein distance 95% confidence intervals over five seeds
Baselines: DyNODE SINDy RNN Transformer Genetic Program G-Sim-ES Abl. ZeroShot G-Sim-ES Abl. ZeroShotOptim
Builds on: WorldCoder evolutionary strategies neural posterior estimation SINDy
Closest papers by meaning
- Model-Free Assessment of Simulator Fidelity via Quantile Curves (NeurIPS 2026 · similarity 0.87)
- Addressing Misspecification in Simulation-based Inference through Data-driven Calibration (ICML 2025 · similarity 0.85)
- Interventionally Consistent Surrogates for Complex Simulation Models (NeurIPS 2024 · similarity 0.85)
- MF-LLM: Simulating Population Decision Dynamics via a Mean-Field Large Language Model Framework (NeurIPS 2025 · similarity 0.84)
- Uncertainty Quantification for LLM-Based Survey Simulations (ICML 2025 · similarity 0.84)
- Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling (NeurIPS 2025 · similarity 0.84)
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