aiqbench analysis
This research introduces MeLISA, a novel autoregressive generative model designed to forecast complex fluid dynamics without relying on iterative diffusion solvers or latent encoders. By leveraging pixel-space MeanFlow and specific consistency losses, the method achieves efficient one-step generation that preserves long-term statistical structures in high-resolution turbulent flows. The approach offers a significant efficiency gain over traditional neural operators while maintaining superior accuracy for extended horizon predictions.
Autoregressive One-Step Generative Modeling for Dynamical System Forecasting
arXiv:2605.05540v2 Announce Type: replace Abstract: Fast surrogate modeling for high-dimensional physical dynamics requires more than low short-term error: useful models must roll out efficiently while preserving the statistical structure of long trajectories. Neural operators provide inexpensive autoregressive forecasts but can drift in turbulent regimes, whereas rolling diffusion and latent generative surrogates can represent stochastic transitions at the cost of multi-step denoising, noise-schedule design, or auxiliary compression models. We propose MeanFlow Long-term Invariant Spatiotemporal Consistency Autoregressive Models (MeLISA), a latent-free autoregressive generative surrogate built on pixel-space MeanFlow. MeLISA defines a blockwise stochastic transition kernel that generates each forecast block with a single model evaluation, avoiding latent encoders and iterative diffusion solvers at inference time. To stabilize long-horizon rollouts, MeLISA combines a Window-Consistency MeanFlow objective that learns conditional spatiotemporal generation from partially observed temporal windows with a Time Increment Consistency loss that constrains multi-lag finite increments and targets temporal-correlation structure. We evaluate MeLISA with compact UNet and scalable DiT backbones on two high-resolution benchmarks, extended 2D Kolmogorov flow at $256 \times 256$ and turbulent channel-flow slice at $192 \times 192$. MeLISA outperforms neural-operator baselines on short-term forecasting accuracy and long-horizon statistical metrics, including energy spectra, turbulent kinetic energy, and mixing-rate-related dynamics, while achieving inference speeds comparable to, and in some cases faster than, neural operators. To our knowledge, this is the first method for high-resolution one-step generation for physical dynamical systems with performance comparable to state-of-the-art deterministic surrogates.
Abstract:Fast surrogate modeling for high-dimensional physical dynamics requires more than low short-term error: useful models must roll out efficiently while preserving the statistical structure of long trajectories. Neural operators provide inexpensive autoregressive forecasts but can drift in turbulent regimes, whereas rolling diffusion and latent generative surrogates can represent stochastic transitions at the cost of multi-step denoising, noise-schedule design, or auxiliary compression models. We propose MeanFlow Long-term Invariant Spatiotemporal Consistency Autoregressive Models (MeLISA), a latent-free autoregressive generative surrogate built on pixel-space MeanFlow. MeLISA defines a blockwise stochastic transition kernel that generates each forecast block with a single model evaluation, avoiding latent encoders and iterative diffusion solvers at inference time. To stabilize long-horizon rollouts, MeLISA combines a Window-Consistency MeanFlow objective that learns conditional spatiotemporal generation from partially observed temporal windows with a Time Increment Consistency loss that constrains multi-lag finite increments and targets temporal-correlation structure. We evaluate MeLISA with compact UNet and scalable DiT backbones on two high-resolution benchmarks, extended 2D Kolmogorov flow at $256 \times 256$ and turbulent channel-flow slice at $192 \times 192$. MeLISA outperforms neural-operator baselines on short-term forecasting accuracy and long-horizon statistical metrics, including energy spectra, turbulent kinetic energy, and mixing-rate-related dynamics, while achieving inference speeds comparable to, and in some cases faster than, neural operators. To our knowledge, this is the first method for high-resolution one-step generation for physical dynamical systems with performance comparable to state-of-the-art deterministic surrogates.
Machine Learning (cs.LG); Fluid Dynamics (physics.flu-dyn)
arXiv:2605.05540 [cs.LG]
(or arXiv:2605.05540v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.05540 Focus to learn more arXiv-issued DOI via DataCite
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