标题： 通过迁移学习和自适应激活函数提高物理信息神经网络的外推能力 显示英文标题

标题： Improving physics-informed neural network extrapolation via transfer learning and adaptive activation functions

摘要： 物理信息神经网络（PINNs）是深度学习模型，它们将系统的控制物理定律融入学习过程，使其非常适合解决复杂的科学和工程问题。 最近，PINNs作为一种将物理原理与数据驱动建模相结合的强大框架，获得了广泛的关注，以提高预测准确性。 然而，尽管取得了成功，PINNs在训练域外的外推性能通常较差，并且对激活函数（AFs）的选择高度敏感。 在本文中，我们引入了一种迁移学习（TL）方法，以提高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（TL），仅使用少量精心选择的配点。 此外，我们提出了一种自适应AF，其形式为标准AF的线性组合，这提高了模型的鲁棒性和准确性。 通过一系列实验，我们证明了我们的方法在不显著增加计算成本的情况下，在外推域中平均减少了40%的相对L2误差和平均减少了50%的平均绝对误差。 代码可在 https://github.com/LiuzLab/PINN-extrapolation 获取。 显示英文摘要

摘要： 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 https://github.com/LiuzLab/PINN-extrapolation .