通过新方法提升物理信息神经网络训练稳定性。
Enhancing Stability of Physics-Informed Neural Network Training Through Saddle-Point Reformulation
- 将PINN训练重构为鞍点问题，优化损失函数复杂性。
- 在多个任务和架构上表现优于现有最先进方法。
- 适合需要高稳定性的科学计算与工程仿真场景。
物理信息神经网络（PINNs）近年来备受关注，已广泛应用于多个领域。然而，其性能仍因损失函数的复杂景观而表现不稳定。为解决此问题，我们将PINN训练重构为非凸-强凹鞍点问题。在建立理论基础后，我们进行了广泛的实验研究，评估该方法在多种任务和网络架构上的有效性。结果表明，所提方法显著优于当前最先进的技术。
原文摘要 · Abstract (English)
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.
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