发表机构
University of Tennessee, Knoxville; McGill University; New York University; Concordia University（田纳西大学诺克斯维尔分校; 麦吉尔大学; 纽约大学; 康考迪亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出尺度分裂神经算子（ScaleSplit-NO），通过父模型预测粗场、子模型预测局部补丁，实现高分辨率三维湍流预测，在精度和数据效率上超越基线，并降低内存消耗。
AI 中文摘要
神经替代模型已成为三维湍流数值模拟的快速替代方案。然而，在高分辨率下训练它们仍然具有挑战性，因为全场模型的内存随分辨率增长。此外，全分辨率训练数据模拟和存储成本高昂，因此稀缺。我们引入了ScaleSplit-NO（尺度分裂神经算子），它利用两个神经算子来利用湍流的尺度结构：父模型预测下一步的全局粗场，子模型基于该预测预测全分辨率的局部补丁。两个模型都不在全分辨率场上运行。子模型单独预训练，然后通过零初始化连接附加到父模型的粗预测上。在两个复杂的高分辨率湍流基准上，ScaleSplit-NO在预测精度和数据效率方面均超越了所有竞争基线。在更高分辨率的JHTDB256（$256^3$）数据集上，其归一化均方误差（NMSE）比最强基线低53%，训练内存比最内存高效的基线低79%。我们进一步展示了其在蒙特利尔真实城区的$500\ imes150\ imes500$网格上的城市风预测有效性，将一步NMSE相对于基线降低了65.8%。此外，交换一个在额外粗场上训练的父模型可以在不重新训练子模型的情况下改善预测，以较小的存储成本提供进一步的精度提升。
英文摘要
Neural surrogates have emerged as fast alternatives to the numerical simulation of three-dimensional turbulence. However, training them at high resolution remains challenging, since the memory of full-field models grows with the resolution. In addition, full-resolution training data are expensive to simulate and store, and therefore scarce. We introduce ScaleSplit-NO (Scale-Split Neural Operator), which exploits the scale structure of turbulence with two neural operators: a Parent predicts the global coarse field at the next time step, and a Child predicts full-resolution local patches conditioned on this prediction. Neither model operates on the full-resolution field. The Child is pretrained alone and then attached to the Parent's coarse prediction through zero-initialized connections. On two complex high-resolution turbulence benchmarks, ScaleSplit-NO surpasses all competing baselines in both prediction accuracy and data efficiency. On the higher-resolution dataset JHTDB256 ($256^3$), its normalized mean squared error (NMSE) is 53% lower than that of the strongest baseline, and its training memory is 79% lower than that of the most memory-efficient baseline. We further demonstrate its effectiveness for urban wind prediction in a real district of Montreal on a $500\times150\times500$ grid, reducing one-step NMSE by 65.8% relative to the baseline. Moreover, swapping in a Parent trained on additional coarse fields improves prediction without retraining the Child, providing further accuracy gains at a small storage cost.
Comments40 pages
