# LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Search

arXiv: https://arxiv.org/abs/2606.25039 · HTML: https://mlsanity.com/paper/2606.25039/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 56 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 30 of 35)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Evolution through Large Models](https://mlsanity.com/paper/2206.08896/) (2022)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [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 with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [Efficient Evolutionary Search Over Chemical Space with Large Language Models](https://mlsanity.com/paper/2406.16976/) (2024)
- [Large Language Models As Evolution Strategies](https://mlsanity.com/paper/2402.18381/) (2024)
- [Towards Scientific Discovery with Generative AI: Progress, Opportunities, and Challenges](https://mlsanity.com/paper/2412.11427/) (2024)
- [SoK: Memorization in General-Purpose Large Language Models](https://mlsanity.com/paper/2310.18362/) (2023)
- [Active Learning for Identification of Linear Dynamical Systems](https://mlsanity.com/paper/2002.00495/) (2020)
- [Optimistic Active Exploration of Dynamical Systems](https://mlsanity.com/paper/2306.12371/) (2023)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [Taylor Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2205.09751/) (2022)
- [LLEMA: Evolutionary Search with LLMs for Multi-Objective Materials Discovery](https://mlsanity.com/paper/2510.22503/) (2025)
- [LLM-AutoSciLab: Closed-Loop Scientific Discovery via Active Experimentation with LLMs](https://mlsanity.com/paper/2605.24043/) (2026)
- [Active Learning Improves Performance on Symbolic RegressionTasks in StackGP](https://mlsanity.com/paper/2202.04708/) (2022)

## Built on by (most cited first, 7 of 7)

- [Autonomous Research Agents: A Survey of AI Scientists and the Verification Gap](https://mlsanity.com/paper/2608.05179/) (2026)
- [Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world models](https://mlsanity.com/paper/2608.09696/) (2026)
- [What Should a Large Language Model See? Physical Invariants as a Data Representation for PDE Discovery](https://mlsanity.com/paper/2608.25189/) (2026)
- [ALDER: Discovering the Laws of a World by Acting in It](https://mlsanity.com/paper/2609.33728/) (2026)
- [Learning to Outgrow a Theory: Experimental Discovery Beyond the Initial Hypothesis Space](https://mlsanity.com/paper/2610.07627/) (2026)
- [LLM-IDEA: Identifiability-Driven Experimental Agent for Autonomous Discovery of Mechanistic World Models](https://mlsanity.com/paper/2610.11253/) (2026)
- [Beyond Equation Search: Conjecture-Guided Discovery with SCOPE and ClosureBench](https://mlsanity.com/paper/2610.18938/) (2026)

## Abstract (arXiv)

Recovering governing Ordinary Differential Equations (ODEs) from data is a central challenge in modeling dynamical systems across scientific domains. Existing approaches cast discovery as a static inference problem over fixed datasets, assuming that the observed trajectories are sufficiently informative. However, dynamical systems evolve over large state spaces, and limited data can make multiple equations observationally indistinguishable, leading to identifiability gaps and the recovery of incorrect governing equations. To address this, we introduce LLM-ACES, or LLM-guided Active Closed-loop Equation Search, a closed-loop framework that jointly optimizes symbolic hypothesis construction and adaptive data acquisition. In LLM-ACES, a large language model (LLM) proposes operator priors that partition the large search space into distinct regions, within which candidate equations are fit to the observed data. The disagreement among these candidates guides the acquisition of informative trajectories, creating a feedback loop that iteratively refines both the hypothesis space and the discovered dynamics. On 122 ODE systems spanning ODEBench and ODEBase, LLM-ACES achieves the lowest median NMSE, outperforming state-of-the-art baselines by several orders of magnitude while achieving a high symbolic accuracy of 46.2% and 52.4%, respectively. Our analysis further shows that LLM-ACES is sample-efficient, achieving better performance with one-tenth the data. Furthermore, LLM-ACES's feedback-driven data acquisition makes it robust to noise and recovers the correct symbolic structure, while baselines introduce spurious terms that fit the data locally but obscure the true governing relationships.