arXiv:2605.05540cs.LGphysics.flu-dyn2026-05

提出无需隐空间的一步生成模型,高效预测复杂物理系统长期演化。

Autoregressive One-Step Generative Modeling for Dynamical System Forecasting

论文配图:Autoregressive One-Step Generative Modeling for Dynamical System Forecasting
图 1 · 摘自论文原文
  • 基于像素空间的均值流,单次推理生成一帧,避免迭代求解与编码器。
  • 在256×256和192×192分辨率下,短期精度与长期统计特性均优于基线模型。
  • 适合需要高速、高保真物理系统模拟的场景,如气象与流体仿真。

高维物理动力系统的快速代理建模不仅要求短期误差低,还需高效滚动预测并保持长轨迹的统计结构。神经算子虽可低成本自回归预测,但在湍流条件下易漂移;而扩散模型和潜在生成代理需多步去噪、噪声调度或辅助压缩模型。本文提出无隐空间的自回归生成代理模型MeLISA,基于像素空间均值流构建块级随机转移核,每块生成仅需一次模型评估,无需推理时的隐编码器或迭代扩散求解器。为稳定长时滚动,引入窗口一致性均值流目标,从部分观测时间窗学习条件时空生成,并结合时间增量一致性损失,约束多滞后有限增量,聚焦时间相关性结构。在两个高分辨率基准上测试:256×256扩展二维科莫戈罗夫流与192×192湍流通道流切片。无论使用紧凑型UNet还是可扩展DiT主干,MeLISA在短期预测准确率与长期统计指标(能量谱、湍流动能、混合率相关动力学)上均超越神经算子基线,且推理速度媲美甚至快于神经算子。据我们所知,这是首个在高分辨率下实现与最先进确定性代理模型相当性能的一步生成方法。

原文摘要 · Abstract (English)

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.

动力系统生成模型物理仿真自回归

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