# LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery

arXiv: https://arxiv.org/abs/2405.09783 · HTML: https://mlsanity.com/paper/2405.09783/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 72 references that are in the map.
- First posted on arXiv 16 May 2024.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 30 of 34)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [Cognitive Architectures for Language Agents](https://mlsanity.com/paper/2309.02427/) (2023)
- [ChemBERTa: Large-Scale Self-Supervised Pretraining for Molecular Property Prediction](https://mlsanity.com/paper/2010.09885/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Large Language Models as Tool Makers](https://mlsanity.com/paper/2305.17126/) (2023)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (2021)
- [Optimization of Molecules via Deep Reinforcement Learning](https://mlsanity.com/paper/1810.08678/) (2018)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [The Impact of Large Language Models on Scientific Discovery: a Preliminary Study using GPT-4](https://mlsanity.com/paper/2311.07361/) (2023)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Empowering Molecule Discovery for Molecule-Caption Translation with Large Language Models: A ChatGPT Perspective](https://mlsanity.com/paper/2306.06615/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)

## Built on by (most cited first, 30 of 86)

- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Review of Large Language Models and Autonomous Agents in Chemistry](https://mlsanity.com/paper/2407.01603/) (2024)
- [Towards Scientific Intelligence: A Survey of LLM-based Scientific Agents](https://mlsanity.com/paper/2503.24047/) (2025)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [LLM Agents for Education: Advances and Applications](https://mlsanity.com/paper/2503.11733/) (2025)
- [Multi-objective Evolution of Heuristic Using Large Language Model](https://mlsanity.com/paper/2409.16867/) (2024)
- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [CodePDE: An Inference Framework for LLM-driven PDE Solver Generation](https://mlsanity.com/paper/2505.08783/) (2025)
- [SR-Scientist: Scientific Equation Discovery With Agentic AI](https://mlsanity.com/paper/2510.11661/) (2025)
- [Optimizing Temperature for Language Models with Multi-Sample Inference](https://mlsanity.com/paper/2502.05234/) (2025)
- [Belief Revision: The Adaptability of Large Language Models Reasoning](https://mlsanity.com/paper/2406.19764/) (2024)
- [PiFlow: Principle-Aware Scientific Discovery with Multi-Agent Collaboration](https://mlsanity.com/paper/2505.15047/) (2025)
- [PhysGym: Benchmarking LLMs in Interactive Physics Discovery with Controlled Priors](https://mlsanity.com/paper/2507.15550/) (2025)
- [LanP: Rethinking the Impact of Language Priors in Large Vision-Language Models](https://mlsanity.com/paper/2502.12359/) (2025)
- [AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2511.07262/) (2025)
- [Gravity-Bench-v1: A Benchmark on Gravitational Physics Discovery for Agents](https://mlsanity.com/paper/2501.18411/) (2025)
- [EngiBench: A Benchmark for Evaluating Large Language Models on Engineering Problem Solving](https://mlsanity.com/paper/2509.17677/) (2025)
- [A Probabilistic Framework for LLM-Based Model Discovery](https://mlsanity.com/paper/2602.18266/) (2026)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physics](https://mlsanity.com/paper/2510.09901/) (2025)
- [Generalists vs. Specialists: Evaluating LLMs on Highly-Constrained Biophysical Sequence Optimization Tasks](https://mlsanity.com/paper/2410.22296/) (2024)
- [Evolving Roles of LLMs in Scientific Innovation: Assistant, Collaborator, Scientist, and Evaluator](https://mlsanity.com/paper/2507.11810/) (2025)
- [Towards Building Specialized Generalist AI with System 1 and System 2 Fusion](https://mlsanity.com/paper/2407.08642/) (2024)
- [From Hypothesis to Publication: A Comprehensive Survey of AI-Driven Research Support Systems](https://mlsanity.com/paper/2503.01424/) (2025)
- [GenoMAS: A Multi-Agent Framework for Scientific Discovery via Code-Driven Gene Expression Analysis](https://mlsanity.com/paper/2507.21035/) (2025)
- [AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing](https://mlsanity.com/paper/2602.17607/) (2026)
- [Grammar-based Game Description Generation using Large Language Models](https://mlsanity.com/paper/2407.17404/) (2024)
- [Adapting While Learning: Grounding LLMs for Scientific Problems with Intelligent Tool Usage Adaptation](https://mlsanity.com/paper/2411.00412/) (2024)

## Abstract (arXiv)

Large Language Models have recently gained significant attention in scientific discovery for their extensive knowledge and advanced reasoning capabilities. However, they encounter challenges in effectively simulating observational feedback and grounding it with language to propel advancements in physical scientific discovery. Conversely, human scientists undertake scientific discovery by formulating hypotheses, conducting experiments, and revising theories through observational analysis. Inspired by this, we propose to enhance the knowledge-driven, abstract reasoning abilities of LLMs with the computational strength of simulations. We introduce Scientific Generative Agent (SGA), a bilevel optimization framework: LLMs act as knowledgeable and versatile thinkers, proposing scientific hypotheses and reason about discrete components, such as physics equations or molecule structures; meanwhile, simulations function as experimental platforms, providing observational feedback and optimizing via differentiability for continuous parts, such as physical parameters. We conduct extensive experiments to demonstrate our framework's efficacy in constitutive law discovery and molecular design, unveiling novel solutions that differ from conventional human expectations yet remain coherent upon analysis.