Transolver-$\sigma$: Joint Spectral-Physical Subspace Modeling for Neural PDE Solving

תקציר מקורי באנגליתarXiv:2609.37279v1 Announce Type: new Abstract: Neural solvers offer efficient surrogates for numerical simulation of partial differential equations (PDEs). For time-dependent problems, strong one-step accuracy does not necessarily translate into reliable autoregressive rollout. We observe that a solver based only on physical-state modeling can achieve lower one-step error, whereas its spectral-only counterpart can become more accurate at later rollout steps. Motivated by this observation, we present Transolver-$\sigma$, a neural PDE solver based on joint spectral--physical subspace modeling. Within each block, adaptive physical-state interactions and spectral transformations are modeled in dedicated latent subspaces, whose responses are recomposed to enable information exchange between th