Threshold Compatibility and Support-Selection Diagnostics in Neural Discovery of Partial Differential Equations

arXiv:2610.37726v1 Announce Type: new Abstract: Accurate regression need not yield the correct equation after support selection. For a median/sample-standard-deviation threshold in neural PDE discovery, we derive an exact two-signal retention boundary and a complete-vector perturbation bound. Exact advection-diffusion libraries lose diffusion despite coefficient recovery to numerical precision. True-support refits of forty saved sparse states reduce diffusion error without restoring all derivative accuracy. A fixed sequential threshold ridge comparator recovers exact support in sixty ideal controls but selects extra terms in every learned state.