mlsanityData to 7 Oct 2026

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

arXiv 2405.09783 ↗First posted 16 May 2024cs.LG cs.AI cs.CEcited by 82

On the map: LLM reasoning → Knowledge- and tool-augmented reasoning

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.

Key facts. Cited by 82 papers in the map (data through 7 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.

Builds on

34 of 72 references.

References · 34

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2022Training language models to follow instructions with human feedbackcited by 15,712
  4. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  5. 2022ReAct: Synergizing Reasoning and Acting in Language Modelscited by 8,355
  6. 2016XGBoost: A Scalable Tree Boosting Systemcited by 5,120
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  9. 2023SGLang: Efficient Execution of Structured Language Model Programscited by 1,107
  10. 2023Large Language Models as Optimizerscited by 830
  11. 2018ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardwarecited by 666
  12. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
22 more
  1. 2023Eureka: Human-Level Reward Design via Coding Large Language Modelscited by 542
  2. 2023Cognitive Architectures for Language Agentscited by 422
  3. 2020ChemBERTa: Large-Scale Self-Supervised Pretraining for Molecular Property Predictioncited by 332
  4. 2019Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradientscited by 294
  5. 2023Large Language Models as Tool Makerscited by 293
  6. 2021Contemporary Symbolic Regression Methods and their Relative Performancecited by 209
  7. 2021ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Predictioncited by 204
  8. 2018Optimization of Molecules via Deep Reinforcement Learningcited by 199
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  11. 2017A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applicationscited by 126
  12. 2023The Impact of Large Language Models on Scientific Discovery: a Preliminary Study using GPT-4cited by 112
  13. 2021SymbolicGPT: A Generative Transformer Model for Symbolic Regressioncited by 101
  14. 2021Symbolic Regression via Neural-Guided Genetic Programming Population Seedingcited by 97
  15. 2023Empowering Molecule Discovery for Molecule-Caption Translation with Large Language Models: A ChatGPT Perspectivecited by 91
  16. 2019Bayesian Symbolic Regressioncited by 77
  17. 2021DiffPD: Differentiable Projective Dynamicscited by 62
  18. 2023Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamicscited by 56
  19. 2018Learning concise representations for regression by evolving networks of treescited by 33
  20. 2022RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimationcited by 29
  21. 2021A General Descent Aggregation Framework for Gradient-based Bi-level Optimizationcited by 28
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 13; 2025: 42; 2026: 27.

82 papers.

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  1. 2025Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Modelscited by 291
  2. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
  3. 2024A Review of Large Language Models and Autonomous Agents in Chemistrycited by 96
  4. 2025Towards Scientific Intelligence: A Survey of LLM-based Scientific Agentscited by 96
  5. 2024A Systematic Survey on Large Language Models for Algorithm Designcited by 65
  6. 2025LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Modelscited by 61
  7. 2025LLM Agents for Education: Advances and Applicationscited by 59
  8. 2024Multi-objective Evolution of Heuristic Using Large Language Modelcited by 52
  9. 2026A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agentscited by 47
  10. 2025CodePDE: An Inference Framework for LLM-driven PDE Solver Generationcited by 37
  11. 2025Optimizing Temperature for Language Models with Multi-Sample Inferencecited by 33
  12. 2025SR-Scientist: Scientific Equation Discovery With Agentic AIcited by 30
38 more
  1. 2024Belief Revision: The Adaptability of Large Language Models Reasoningcited by 26
  2. 2025PiFlow: Principle-Aware Scientific Discovery with Multi-Agent Collaborationcited by 25
  3. 2025LanP: Rethinking the Impact of Language Priors in Large Vision-Language Modelscited by 14
  4. 2025Gravity-Bench-v1: A Benchmark on Gravitational Physics Discovery for Agentscited by 13
  5. 2025PhysGym: Benchmarking LLMs in Interactive Physics Discovery with Controlled Priorscited by 13
  6. 2025AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learningcited by 13
  7. 2025Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physicscited by 11
  8. 2025EngiBench: A Benchmark for Evaluating Large Language Models on Engineering Problem Solvingcited by 10
  9. 2026A Probabilistic Framework for LLM-Based Model Discoverycited by 10
  10. 2025Evolving Roles of LLMs in Scientific Innovation: Assistant, Collaborator, Scientist, and Evaluatorcited by 9
  11. 2025A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solvingcited by 9
  12. 2024Towards Building Specialized Generalist AI with System 1 and System 2 Fusioncited by 8
  13. 2024Generalists vs. Specialists: Evaluating LLMs on Highly-Constrained Biophysical Sequence Optimization Taskscited by 8
  14. 2025From Hypothesis to Publication: A Comprehensive Survey of AI-Driven Research Support Systemscited by 8
  15. 2024Grammar-based Game Description Generation using Large Language Modelscited by 7
  16. 2024Adapting While Learning: Grounding LLMs for Scientific Problems with Intelligent Tool Usage Adaptationcited by 7
  17. 2025Exploiting Edited Large Language Models as General Scientific Optimizerscited by 7
  18. 2026AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computingcited by 7
  19. 2024GDSG: Graph Diffusion-based Solution Generator for Optimization Problems in MEC Networkscited by 6
  20. 2025MOOSE-Chem3: Toward Experiment-Guided Hypothesis Ranking via Simulated Experimental Feedbackcited by 6
  21. 2025GenoMAS: A Multi-Agent Framework for Scientific Discovery via Code-Driven Gene Expression Analysiscited by 6
  22. 2025Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula Discoverycited by 6
  23. 2025EAIRA: Establishing a Methodology for Evaluating AI Models as Scientific Research Assistantscited by 5
  24. 2025Conversational Education at Scale: A Multi-LLM Agent Workflow for Procedural Learning and Pedagogic Quality Assessmentcited by 5
  25. 2025Deep Ideation: Designing LLM Agents to Generate Novel Research Ideas on Scientific Concept Networkcited by 5
  26. 2025Embodied Co-Design for Rapidly Evolving Agents: Taxonomy, Frontiers, and Challengescited by 4
  27. 2026LLM-Based Scientific Equation Discovery via Physics-Informed Token-Regularized Policy Optimizationcited by 4
  28. 2026AutoSci: A Memory-Centric Agentic System for the Full Scientific Research Lifecyclecited by 4
  29. 2024Synthesizing Interpretable Control Policies through Large Language Model Guided Searchcited by 3
  30. 2025A Status Quo Investigation of Large Language Models towards Cost-Effective CFD Automation with OpenFOAMGPT: ChatGPT vs. Qwen vs. Deepseekcited by 3
  31. 2025Efficient Knowledge Probing of Large Language Models by Adapting Pre-trained Embeddingscited by 3
  32. 2025VisionLaw: Inferring Interpretable Intrinsic Dynamics from Visual Observations via Bilevel Optimizationcited by 3
  33. 2025Instructional Agents: Reducing Teaching Faculty Workload through Multi-Agent Instructional Designcited by 3
  34. 2025SimulRAG: Simulator-based RAG for Grounding LLMs in Long-form Scientific QAcited by 3
  35. 2025Automated Model Discovery via Multi-modal & Multi-step Pipelinecited by 3
  36. 2026Data-driven discovery of governing differential equations across physical systemscited by 3
  37. 2025A Survey of Large Language Models in Discipline-specific Research: Challenges, Methods and Opportunitiescited by 2
  38. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2

50 most cited of 82 All 82 (JSON)

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  2. 2025NewtonBench: Benchmarking Generalizable Scientific Law Discovery in LLM Agents
  3. 2026The Little Scientist: LLM Agent-Driven Discovery via the Scientific Method
  4. 2026Molecular LLM Agents: From Architectural Design to Scientific Autonomy
  5. 2025Advancing AI-Scientist Understanding: Multi-Agent LLMs with Interpretable Physics Reasoning
  6. 2026DiscoverPhysics: Benchmarking LLMs for Out-of-the-Box Scientific Thinking
  7. 2025BoxingGym: Benchmarking Progress in Automated Experimental Design and Model Discovery
  8. 2025From AI for Science to Agentic Science: A Survey on Autonomous Scientific Discovery