提升神经算子长期预测稳定性，通过守恒量修正解决误差累积问题。
Benchmarking Long Roll-outs of Auto-regressive Neural Operators for the Compressible Navier-Stokes Equations with Conserved Quantity Correction
- 引入守恒量修正技术，通用性地增强模型物理一致性。
- 长期预测误差显著降低，跨架构均表现稳定提升。
- 揭示现有模型对高频分量建模不足，适合流体模拟研究者。
深度学习被提出作为偏微分方程数值解的高效替代方案，通过近似解算子实现快速迭代模拟。然而，由于自回归误差积累及模型无法保持物理守恒量，深度学习方法在长时序预测中表现不佳。本文提出一种模型无关的守恒量修正技术，将物理守恒约束融入深度学习模型。实验表明，该方法显著提升了自回归神经算子的长期稳定性，且不依赖具体模型架构。此外，我们从谱域分析神经算子性能，揭示现有架构在高频率成分建模上的显著局限。结果强调未来工作应关注能更好捕捉湍流关键高频特征的网络设计。
原文摘要 · Abstract (English)
Deep learning has been proposed as an efficient alternative for the numerical approximation of PDE solutions, offering fast, iterative simulation of PDEs through the approximation of solution operators. However, deep learning solutions have struggle to perform well over long prediction durations due to the accumulation of auto-regressive error, which is compounded by the inability of models to conserve physical quantities. In this work, we present conserved quantity correction, a model-agnostic technique for incorporation physical conservation criteria within deep learning models. Our results demonstrate consistent improvement in the long-term stability of auto-regressive neural operator models, regardless of the model architecture. Furthermore, we analyze the performance of neural operators from the spectral domain, highlighting significant limitations of present architectures. These results highlight the need for future work to consider architectures that place specific emphasis on high frequency components, which are integral to the understanding and modeling of turbulent flows.
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