Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow
Deep learning paradigms, such as PINNs and neural operators, have significantly advanced the solving of PDEs. However, they often struggle to capture the continuous integral nature of physical systems, relying either on pointwise residuals that ignore the integral perspective or on pre-discretized temporal grids. Drawing inspiration from MeanFlow, a continuous-time integrator recently developed to efficiently solve generative ODEs, we introduce Spatio-Temporal MeanFlow, which functions as a novel PDE solver learning the finite-interval evolution of physical states. By substituting the generative velocity field with the physical PDE operator, we transform multi-step numerical integration i...
| Authors | Hanru Bai, Yuncheng Zhou, Difan Zou |
|---|---|
| Primary category | cs.LG |
| Published | 9 May 2026 |
| Last updated at source | 9 May 2026 |
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