LADS: LLM-guided Ansatz Discovery for Symbolic PDE Solutions

Finding PDE solutions from the governing equation and its initial and boundary conditions is a fundamental challenge when the global solution structure is unknown. Existing symbolic pipelines often ask a practitioner to supply a high-level Ansatz in advance; however, when that structure is unknown it is rarely available a priori. To address this gap, we propose LADS: an LLM proposes an atom-free Ansatz; a verification module accepts or rejects it; Atoms are generated only for open slots of an accepted Ansatz; coefficients are fitted and selected by residuals of the PDE and the prescribed conditions. On a manufactured development catalog, accuracy tracks whether the proposed Ansatz recovers a usable structure: later stages finish a recovered family but do not repair a miss. We report this as a controlled in-sample diagnostic, not as generalization to a sealed holdout. Our code is available at \url{https://anonymous.4open.science/r/LADS/}.