The conventional numerical solvers for partial differential equations encounter a formidable challenge, as their computational efficiency and accuracy are heavily contingent on grid size. Recently, machine learning (ML) has exhibited substantial promise in addressing partial differential equations. Nevertheless, substantial hurdles persist in practical applications. In this work, we endeavor to establish a deep learning framework founded on the Fourier neural operator (FNO) for resolving the intricacies of simulating real landslide dynamic processes. Our findings demonstrate that the current FNO approach adeptly replicates landslide dynamic processes and boasts exceptional computational efficiency. Additionally, it is noteworthy that this data-driven ML methodology can seamlessly incorporate data from other experimental sources or numerical simulation techniques. Consequently, this work underscores the significant potential of utilizing ML methodologies to supplant conventional numerical simulation methods.

中文翻译：

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基于傅里叶神经算子的真实滑坡动态过程建模深度学习方法

偏微分方程的传统数值求解器遇到了巨大的挑战，因为它们的计算效率和精度在很大程度上取决于网格大小。最近，机器学习 (ML) 在解决偏微分方程方面展现出了巨大的前景。然而，在实际应用中仍然存在很大的障碍。在这项工作中，我们致力于建立一个基于傅里叶神经算子（FNO）的深度学习框架，以解决模拟真实滑坡动态过程的复杂性。我们的研究结果表明，当前的 FNO 方法能够熟练地复制滑坡动态过程，并拥有卓越的计算效率。此外，值得注意的是，这种数据驱动的机器学习方法可以无缝整合来自其他实验来源或数值模拟技术的数据。因此，这项工作强调了利用机器学习方法取代传统数值模拟方法的巨大潜力。