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

Researchers introduce LLM-ACES, a framework combining large language models with active learning to discover governing equations of dynamical systems from data. The approach achieves significant improvements in accuracy and sample efficiency by using LLM-proposed hypotheses to guide strategic data acquisition, outperforming existing methods on 122 ODE systems while requiring substantially less training data.

LLM-ACES represents a meaningful advance in scientific machine learning by addressing a fundamental challenge in dynamical systems discovery. Traditional equation recovery methods treat data as static inputs and attempt to infer governing equations through fixed optimization procedures. This approach fails when observational data proves insufficient to distinguish between multiple mathematically valid equations—a common scenario in complex systems with large state spaces. The research demonstrates how LLMs can provide valuable inductive bias by generating operator priors that organize the hypothesis search space, while active learning mechanisms identify which additional experiments or simulations would most effectively resolve remaining ambiguities.

The framework's closed-loop architecture creates a feedback mechanism where disagreement among competing equation candidates directly informs data acquisition strategy. Rather than collecting random or uniform trajectories, the system targets sampling regions where different hypotheses diverge most significantly. This principled approach to adaptive experimentation mirrors scientific practice and dramatically improves sample efficiency—achieving comparable performance with one-tenth the data compared to baseline methods.

The quantitative results on 122 systems are particularly noteworthy, with symbolic accuracy reaching 46-52% while maintaining orders-of-magnitude improvements in numerical prediction error. The robustness to noise suggests the framework recovers genuine structural relationships rather than merely fitting local patterns with spurious terms. This has implications for scientific discovery across domains from physics to biology where obtaining high-quality data is expensive or constrained.

For the broader machine learning community, LLM-ACES validates the value of hybrid approaches combining neural language models with principled active learning. The work establishes a template for integrating foundation models into scientific workflows where human-interpretable symbolic outputs remain essential.

• →LLM-ACES combines language model reasoning with active learning to discover dynamical system equations with 46-52% symbolic accuracy on benchmark tests.
• →The framework achieves superior performance while requiring one-tenth the data of competing methods through intelligent feedback-driven data acquisition.
• →Active learning components resolve identifiability problems by targeting data collection where competing hypotheses most strongly disagree.
• →Results demonstrate robustness to noise and recovery of true governing structures, avoiding spurious terms that fit but misrepresent underlying dynamics.
• →The approach generalizes across 122 distinct ODE systems, indicating broad applicability for scientific discovery tasks.