M³ Framework Reduces Bias in Neural Physical Simulations

A new framework called M³ (Multi-scale Morton Measure) has been introduced by researchers to address bias caused by measures in neural surrogate models used for physical simulations. These models rely on discretized samples from continuous domains, leading to spatial inconsistencies due to uneven empirical measure supervision. M³ enhances training by dividing space based on physical variations and distributing supervision across various scales. Evaluated on three industrial-scale datasets with differing discretizations, M³ consistently delivers better predictions, with errors reduced by as much as 4.7× in large volumetric scenarios. The improvements remain significant even with aggressive subsampling (160M → 16M → 1.6M points), where M³-trained models surpass those trained on higher-resolution data, achieving a 3–4× reduction in physics-weighted relative L2 error.