# Uncertainty-Aware Simulation-Based Inference for Operations Research with Large Language Models

arXiv: https://arxiv.org/abs/2608.00019 · HTML: https://mlsanity.com/paper/2608.00019/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)
- [DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models](https://mlsanity.com/paper/2309.03883/) (2023)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learning](https://mlsanity.com/paper/2511.09092/) (2025)
- [Entropy-Tree: Tree-Based Decoding with Entropy-Guided Exploration](https://mlsanity.com/paper/2601.15296/) (2026)

## Abstract (arXiv)

Deploying large language models (LLMs) for operations research (OR) tasks remains challenging because correctness depends on a coherent modeling process, not merely a correct final answer. Standard autoregressive generation operates on a myopic policy, which sometimes fails to anticipate whether a partial formulation can be validly extended into a globally consistent optimization model. Consequently, locally plausible steps may propagate into catastrophic downstream formulation or solver code errors. To address this, we propose an uncertainty-aware, training-free inference framework for OR mathematical modeling. Without updating model parameters, our method evaluates intermediate candidate steps using short lookahead simulations to quantify downstream predictive uncertainty or probability concentration. Candidates that demonstrate a higher likelihood of yielding coherent mathematical formulations are then dynamically selected via importance resampling. Empirical evaluations across multiple OR benchmarks (including NL4OPT, MAMO, and IndustryOR) demonstrate that our framework consistently outperforms both standard and low-temperature baselines, establishing an efficient, training-free paradigm for reliable OR formulation generation.