用多尺度隐式网络提升流体模拟长期预测稳定性
Hierarchical Implicit Neural Emulators
- 通过分层未来状态压缩表示，实现多粒度动态建模
- 在湍流模拟中长期预测误差显著低于自回归模型
- 计算开销小，适合需要稳定长时模拟的场景
神经偏微分方程求解器虽能建模复杂动力系统，但常在长时间跨度下出现误差累积、不稳定及物理不一致问题。本文提出一种分层隐式神经模拟器，通过条件化一系列低维未来状态表示来增强长期预测精度。受数值隐式时间步进方法稳定性的启发，该方法在不同压缩率下预测多步未来状态，用于下一时刻的精细化修正。通过主动调整时间下采样比率，模型可捕捉多尺度动态并保证长程时间一致性。在湍流流体动力学实验中，本方法在保持高短期精度的同时实现长期稳定预测，显著优于自回归基线，且计算开销增加极小。
原文摘要 · Abstract (English)
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit neural emulator that enhances long-term prediction accuracy by conditioning on a hierarchy of lower-dimensional future state representations. Drawing inspiration from the stability properties of numerical implicit time-stepping methods, our approach leverages predictions several steps ahead in time at increasing compression rates for next-timestep refinements. By actively adjusting the temporal downsampling ratios, our design enables the model to capture dynamics across multiple granularities and enforce long-range temporal coherence. Experiments on turbulent fluid dynamics show that our method achieves high short-term accuracy and produces long-term stable forecasts, significantly outperforming autoregressive baselines while adding minimal computational overhead.
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