标题： 通过鞍点重表述提高物理信息神经网络训练的稳定性 显示英文标题

标题： Enhancing Stability of Physics-Informed Neural Network Training Through Saddle-Point Reformulation

摘要： 物理信息神经网络（PINNs）近年来获得了关注，并现在被有效地用于许多应用中。 然而，由于损失函数的复杂性，它们的性能仍然不稳定。 为了解决这个问题，我们将PINN训练重新表述为一个非凸-强凹的鞍点问题。 在建立该方法的理论基础后，我们进行了广泛的实验研究，评估其在各种任务和架构中的有效性。 我们的结果表明，所提出的方法优于当前最先进的技术。 显示英文摘要

摘要： Physics-informed neural networks (PINNs) have gained prominence in recent years and are now effectively used in a number of applications. However, their performance remains unstable due to the complex landscape of the loss function. To address this issue, we reformulate PINN training as a nonconvex-strongly concave saddle-point problem. After establishing the theoretical foundation for this approach, we conduct an extensive experimental study, evaluating its effectiveness across various tasks and architectures. Our results demonstrate that the proposed method outperforms the current state-of-the-art techniques.