用扩散模型稳定神经模拟器的长期预测，突破混沌系统预测瓶颈。
Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos
- 引入扩散模型估计系统不变测度的梯度，实现推理时动态去噪。
- 在复杂混沌系统中将稳定预测时间延长一个数量级。
- 适合需要长时程仿真的物理建模与工程系统设计者。
自回归代理模型（或称模拟器）为时空系统的快速近似预测提供了途径，广泛应用于科学与工程领域。然而，在推理阶段，由于误差累积导致轨迹发散，这些模型通常无法进行长时间预测。本质上，模拟器运行于分布外，且在大规模场景下在线分布控制变得不可行。针对这一根本问题，我们聚焦于具有不变测度的时间平稳系统，利用扩散模型获得该不变测度的隐式梯度估计。我们证明，该梯度函数可用于在推理过程中实施即时去噪，这一过程称为“热化”（thermalization），从而稳定自回归模拟器的推演。实验表明，在表现出湍流和混沌行为的复杂系统中，热化可使稳定预测时间延长一个数量级，开创了扩散模型在神经模拟中的新应用。
原文摘要 · Abstract (English)
Autoregressive surrogate models (or \textit{emulators}) of spatiotemporal systems provide an avenue for fast, approximate predictions, with broad applications across science and engineering. At inference time, however, these models are generally unable to provide predictions over long time rollouts due to accumulation of errors leading to diverging trajectories. In essence, emulators operate out of distribution, and controlling the online distribution quickly becomes intractable in large-scale settings. To address this fundamental issue, and focusing on time-stationary systems admitting an invariant measure, we leverage diffusion models to obtain an implicit estimator of the score of this invariant measure. We show that this model of the score function can be used to stabilize autoregressive emulator rollouts by applying on-the-fly denoising during inference, a process we call \textit{thermalization}. Thermalizing an emulator rollout is shown to extend the time horizon of stable predictions by an order of magnitude in complex systems exhibiting turbulent and chaotic behavior, opening up a novel application of diffusion models in the context of neural emulation.
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