Temporal coherency in high-resolution 3D neural PDE surrogates
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Transformer-based neural networks can accurately learn the spatial dynamics of partial differential equations, but modeling turbulent Navier-Stokes flows requires capturing both spatial structure and long-term temporal evolution across multiple scales. Here, we assess the P3D model for high-resolution three-dimensional turbulence, comparing deterministic and diffusion-based training for autoregressive predictions. Our results show that probabilistic training improves the representation of energy across scales and stabilizes long-term predictions, providing guidance for reliable neural surrogates of chaotic flows.
