Scale-Split Neural Operator for Memory- and Data-Efficient 3D Turbulence Prediction

2026-09-30

AI Summary

This study addresses the prohibitive memory overhead and data scarcity in training high-resolution 3D turbulence neural surrogate models by proposing the ScaleSplit-NO framework. This method introduces a novel parent–child operator decoupling architecture that employs a dual-operator structure to separate global coarse-field from local fine-field predictions, thereby circumventing full-resolution computation. Following pre-training, the child operator is integrated into the parent operator with zero-initialized weights, enhancing prediction accuracy by supplementing coarse-field information without requiring retraining. Experimental evaluations demonstrate that the proposed model reduces the normalized mean squared error (NMSE) by 53% and memory consumption by 79% on the JHTDB256 benchmark. Furthermore, it decreases prediction error by 65.8% for urban wind field forecasting in Montreal, achieving efficient and accurate turbulence modeling.

Abstract

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.

Problem

• 3D turbulence prediction
• neural surrogate
• memory efficiency
• data efficiency
• high-resolution training

Innovation

• Neural Operator
• Scale-Split Architecture
• 3D Turbulence Prediction
• Memory Efficiency
• Data Efficiency