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

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 $500\times 150\times 500$ 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. Our code is included in the supplementary material.