סמל המחליף: מדידת תצורה מספרית בפתרוני PDE נוירלי

תקציר מקורי באנגליתarXiv:2610.09255v1 Announce Type: new Abstract: Neural PDE surrogates are trained on numerical solver outputs that contain both physical evolution and solver-specific discretization errors. Because surrogates are also evaluated against held-out trajectories from the same solver, standard benchmarks cannot distinguish fidelity to the exact evolution from imitation of the numerical scheme. We introduce an empirical Fourier-symbol diagnostic that probes a trained surrogate's linearized one-step operator with individual Fourier modes and compares it with both exact-evolution and training-scheme references. To address architectural spectral bias, we train identical networks on schemes with orthogonal dissipative and dispersive signatures and compare their learned operators. In linear advection,