停留在吸引子上：在神经代理模型偏离三维湍流吸引子处进行监督
Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave It
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中文总结 AI 辅助
针对神经代理模型预测三维湍流时偏离吸引子导致失效的问题，提出偏离吸引子监督（OAS），通过DNS重标注代理模型可能失败的状态，将中位失效时间从21步提升至721步，并改善统计保真度。
中文摘要 AI 辅助
神经代理模型被训练用于预测三维湍流，以替代直接数值模拟（DNS）。对于混沌流动，目标是实现短期的逐点准确性，随后保持长期的物理和统计保真度。然而，小的预测误差可能使代理模型偏离流动的吸引子。偏离吸引子的状态在训练数据中表示不足，导致其演化的约束较弱。学习到的动力学可能放大偏差，导致发散、冻结或统计漂移。我们提出偏离吸引子监督（OAS），在代理模型偏离吸引子的位置对其进行监督。OAS教会模型从这些状态出发，真实的纳维-斯托克斯动力学将如何演化。每个选定的状态都与通过DNS计算的其自身未来配对。三个生成器选择几百个状态进行重新标注。第一个生成器从代理模型自身的滚动中收集状态。第二个使用代理攻击来针对冻结、过度放大以及违反不可压缩性和能量平衡的情况。第三个生成器沿着动力学的一个放大方向和一个强阻尼随机方向扰动训练状态。所有攻击仅针对代理模型运行，DNS重新标注对每个选定状态离线执行一次。在128^3湍流上的实验表明，OAS将中位失效时间从21步增加到721步。对比的基线方法中位数最多为110步，且该优势在不同训练种子下均保持。OAS在步骤15时也实现了最低的逐点误差，并在对比方法中获得了最佳的长时统计。OAS通过将监督从固定参考轨迹扩展到代理模型可能失败的状态，将物理模型整合到神经模拟中。这一原则可以指导在部署超出训练数据覆盖范围时开发更可靠的科学代理模型。
英文摘要
Neural surrogates are trained to predict 3D turbulent flows in place of direct numerical simulation (DNS). For chaotic flows, the goal is short-term pointwise accuracy followed by long-term physical and statistical fidelity. However, small prediction errors can carry a surrogate away from the flow's attractor. Off-attractor states are poorly represented in training data, leaving their evolution weakly constrained. The learned dynamics can then amplify deviations and lead to blow-up, freezing, or statistical drift. We propose off-attractor supervision (OAS) to supervise neural surrogates where they leave the attractor. OAS teaches the model how the true Navier-Stokes dynamics would evolve from these states. Each selected state is paired with its own future computed by DNS. Three generators select a few hundred states for relabeling. The first collects states from the surrogate's own rollouts. The second uses surrogate attacks to target freezing, excessive amplification, and violations of incompressibility and energy balance. The third perturbs training states along an amplified direction and a strongly damped random direction of the dynamics. All attacks run on the surrogate alone, and DNS relabeling is performed offline once per selected state. Experiments on $128^3$ turbulence show that OAS increases the median time to failure from 21 to 721 steps. The compared baselines achieve medians of at most 110 steps, and the advantage holds across training seeds. OAS also achieves the lowest pointwise error at step 15 and the best long-horizon statistics among the compared methods. OAS integrates physical models into neural simulation by extending supervision from fixed reference trajectories to states where the surrogate is likely to fail. This principle can guide the development of more reliable scientific surrogates when deployment takes models beyond the coverage of their training data.
