How AI Agents Discover Scientific Equations: From Hydrotope Rediscovery to New Water-Wave Amplitudes

The paper investigates how AI agents can discover and validate scientific formulas, focusing on the hydrotope—a geometric formula that unifies polynomial pieces of nonlinear surface-wave scattering. Through controlled experiments, the authors compare human–agent collaboration, single-prompt rediscovery, and various guided approaches, finding that only a PI$+$two-student workflow reliably reconstructs the full hydrotope and even uncovers a new analytic expression for the six-point amplitude $A_6$. The study highlights the challenges of combining exponentially many terms and the importance of coordinated analytic and numerical tasks for successful formula discovery.

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