Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods involve such conditions in computations without needing to learn them. In this study, we propose to improve current physics-informed deep learning strategies such that initial and/or boundary conditions do not need to be learned and are represented exactly in the predicted solution. Moreover, this method guarantees that when a deep operator network is applied multiple times to time-step a solution of an initial value problem, the resulting function is at least continuous.

翻译：当前的物理信息（标准或深度算子）神经网络仍需精确学习其所求解微分方程系统的初始条件和/或边界条件。相比之下，标准数值方法在计算中直接包含这些条件而无需学习它们。本研究提出改进现有物理信息深度学习策略，使得初始条件和/或边界条件无需学习即可在预测解中获得精确表示。此外，该方法确保当深度算子网络多次应用于初值问题的时间步进求解时，所得函数至少保持连续性。