Decoupling field reconstruction from equation selection—by freezing a learned field representation and then selecting terms via stability-validated weak-form analysis—improves PDE discovery from sparse observations compared to end-to-end neural approaches.
This paper tackles PDE discovery from sparse data by separating field reconstruction from equation selection. The authors develop a freeze-then-select method that first trains a neural adapter to reconstruct the continuous field, then uses stability-validated weak selection to identify the correct differential terms.