通过迁移学习与自适应激活函数提升PINN外推能力
Improving physics-informed neural network extrapolation via transfer learning and adaptive activation functions
- 在扩展训练域上用少量采样点做迁移学习，增强外推性能
- 外推域相对L2误差平均降低40%，绝对误差平均降低50%
- 适合需高精度外推的物理建模场景，如流体力学与结构力学
物理信息神经网络（PINNs）将系统控制的物理定律融入学习过程，适用于解决复杂的科学与工程问题。尽管取得显著进展，但PINNs在训练域外常表现出较差的外推性能，且对激活函数选择高度敏感。本文提出一种迁移学习方法，在扩展训练域上仅使用少量精心选取的采样点进行训练；同时引入一种由标准激活函数线性组合而成的自适应激活函数，提升模型鲁棒性与准确性。实验表明，该方法在不显著增加计算成本的前提下，使外推域的相对L2误差平均降低40%，均方绝对误差平均降低50%。代码已公开于 https://github.com/LiuzLab/PINN-extrapolation。
原文摘要 · Abstract (English)
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 .
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