Transolver-$σ$: Joint Spectral-Physical Subspace Modeling for Neural PDE Solving
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-$σ$, 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 re...
| Authors | Haonan Shangguan, Hang Zhou, Haixu Wu et al. |
|---|---|
| Primary category | cs.AI |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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