LLM-ACES Discovers Dynamical Systems with Adaptive Search.

Recovering the governing Ordinary Differential Equations (ODEs) from observed data is a fundamental challenge across various scientific and engineering disciplines. Existing methods typically treat this as a static inference problem, assuming the available data trajectories are sufficiently informative. However, dynamical systems often operate in vast state spaces, and limited data can lead to multiple observationally indistinguishable equations, resulting in identifiability gaps and incorrect model recovery. To overcome these limitations, researchers introduce LLM-ACES (LLM-guided Active Closed-loop Equation Search). This framework operates in a closed-loop, dynamically optimizing both the construction of symbolic hypotheses and the adaptive acquisition of new data. Within LLM-ACES, a large language model (LLM) proposes operator priors, effectively partitioning the extensive search space into manageable regions. Candidate equations are then fitted to the observed data within these regions. The disagreement among these candidate equations serves as a guide for acquiring more informative trajectories, establishing a feedback loop that iteratively refines both the hypothesis space and the discovered dynamics. Evaluated on 122 ODE systems from ODEBench and ODEBase, LLM-ACES achieved the lowest median Normalized Mean Squared Error (NMSE), outperforming state-of-the-art baselines by several orders of magnitude. It also demonstrated high symbolic accuracy (46.2% and 52.4%) and remarkable sample efficiency, achieving better performance with only one-tenth of the data. Furthermore, its feedback-driven data acquisition makes it robust to noise, accurately recovering true symbolic structures where baselines might introduce spurious terms.