ALDER: Discovering the Laws of a World by Acting in It
This study addresses the limitation of fixed trajectories or predefined candidate sets in distinguishing competing hypotheses and discovering novel equations. To this end, it proposes ALDER, a method that refines explicit equation-based world models through an iterative mechanism of active experimentation, fitting, and validation, thereby enabling interactive physical law discovery and control. The core innovation lies in introducing a cost- and safety-aware intervention selector that dynamically generates experiments to differentiate hypotheses and update an evidence ledger, transcending the constraints of the initial hypothesis space. In both benchmark evaluations and robotic experiments, ALDER surpasses predefined formula sets by significantly reducing interaction counts, improving out-of-distribution prediction accuracy, and supporting goal-directed control.