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

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, implicitly assuming that the observed trajectories are sufficiently informative. However, dynamical systems evolve over large state spaces, and limited data can often fit multiple distinct equations that explain the observations equally well, leading to identifiability gaps and incorrect recovery of the true dynamics. We introduce LLM-ACES or LLM-guided Active Closed-loop Equation Search, a closed-loop framework that jointly optimizes data acquisition and hypothesis generation under a constrained simulation budget. LLM-ACES leverages LLMs to construct structured, domain-informed hypothesis spaces via a two-stage process: high-level prior induction followed by candidate equation generation within each prior. To resolve ambiguity among competing hypotheses, we introduce an active data selection strategy that identifies regions of maximal predictive divergence among candidate equations and queries the system to obtain informative trajectories. This induces a feedback loop in which hypotheses guide data acquisition and newly acquired data refine the hypothesis space. Experiments demonstrate that LLM-ACES achieves more accurate equation recovery than prior state-of-the-art methods. Our ablations and analyses highlight the importance of coupling hypothesis construction with feedback-driven data acquisition for reliable discovery of dynamical systems.