Abstract
Physics-Informed Neural Networks (PINNs) are deep learning models that incorporate the governing physical laws of a system into the learning process, making them well-suited for solving complex scientific and engineering problems. Recently, PINNs have gained widespread attention as a powerful framework for combining physical principles with data-driven modeling to improve prediction accuracy. Despite their successes, however, PINNs often exhibit poor extrapolation performance outside the training domain and are highly sensitive to the choice of activation functions (AFs). In this paper, we introduce a transfer learning (TL) method to improve the extrapolation capability of PINNs. Our approach applies transfer learning (TL) within an extended training domain, using only a small number of carefully selected collocation points. Additionally, we propose an adaptive AF that takes the form of a linear combination of standard AFs, which improves both the robustness and accuracy of the model. Through a series of experiments, we demonstrate that our method achieves an average of 40% reduction in relative L2 error and an average of 50% reduction in mean absolute error in the extrapolation domain, all without a significant increase in computational cost. The code is available at this https URL .
Abstract (translated)
物理信息神经网络（Physics-Informed Neural Networks，PINNs）是一种深度学习模型，它将系统的支配物理定律融入到学习过程中，因此非常适合解决复杂的科学和工程问题。近年来，由于能够结合物理原理与数据驱动建模以提高预测准确性，PINNs受到了广泛的关注。尽管取得了成功，但PINNs在训练域之外的外推性能较差，并且对激活函数（AFs）的选择非常敏感。在这篇论文中，我们引入了一种迁移学习（TL）方法来改进PINNs的外推能力。我们的方法在扩展的训练域内应用迁移学习，仅使用少量精心挑选的配置点(collocation points)。此外，我们还提出了一种自适应激活函数，它由标准激活函数以线性组合的形式构成，从而提高了模型的鲁棒性和准确性。通过一系列实验，我们展示了该方法在外推领域中平均减少了40%的相对L2误差和50%的平均绝对误差，而无需显著增加计算成本。代码可在[此处](https://this https URL)获取。
URL
https://arxiv.org/abs/2507.12659
