We investigate a numerical method for approximating the solution of the one dimensional acoustic wave problem, when violating the numerical stability condition. We use deep learning to create an explicit non-linear scheme that remains stable for larger time steps and produces better accuracy than the reference implicit method. The proposed spatio-temporal neural-network architecture is additionally enhanced during training with a physically-informed term, adapting it to the physical problem it is approximating and thus more accurate.

中文翻译：

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超越 Courant-Friedrichs-Lewy 条件：使用深度学习解决波动问题的数值方法

我们研究了一种在违反数值稳定性条件时近似求解一维声波问题的数值方法。我们使用深度学习来创建一个显式非线性方案，该方案在更大的时间步长内保持稳定，并产生比参考隐式方法更好的精度。所提出的时空神经网络架构在训练过程中得到了额外的增强，具有物理信息，使其适应它所逼近的物理问题，从而更准确。