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

翻译：当前的物理信息（标准或算子）神经网络仍依赖于准确学习所求解系统的初始条件。相比之下，标准数值方法在演算此类初始条件时无需对其进行学习。本研究提出改进现有物理信息深度学习策略，使初始条件无需被学习且能在预测解中精确呈现。此外，该方法确保当深度算子网络（DeepONet）被多次应用于对解进行时间步进时，所得函数是连续的。