PriSIFT: Prior-Fitted Structural Inference from Trajectories for Sparse ODE Discovery

Sparse ODE discovery requires identifying a compact governing structure from an exponentially large space of candidate supports. Existing methods solve this structural selection problem independently for each new system, while exhaustive evaluation becomes increasingly costly as the candidate library grows. We introduce PriSIFT, a prior-fitted framework that learns transferable structural regularities from synthetic ODE systems and reuses them to guide discovery on unseen dynamics. Given observed trajectories, a Set-Time Transformer produces term-level structural scores in a single forward pass; these scores define a compact set of plausible support proposals, which are then fitted and verified using task-local extended-BIC rather than a learned final selector. This separation allows cross-system structural knowledge to be amortized while keeping the final scientific decision grounded in the observed data. On a 20-system external literature benchmark held out from method development, PriSIFT achieves the strongest dimension-averaged macro support F1 among evaluated methods (0.678). In matched compute experiments on the fresh holdout, it evaluates 154× fewer candidate supports and achieves a 69× measured wall-clock speedup over exhaustive EBIC. These results suggest that prior-data fitting can provide transferable structural guidance for efficient and reliable equation discovery.