提出新型激活函数REAct，显著提升物理神经网络的精度与泛化能力。
REAct: Rational Exponential Activation for Better Learning and Generalization in PINNs
- 设计可学习参数的有理指数激活函数REAct，增强模型适应性。
- 在热传导问题上误差比tanh低三个数量级，且对更细网格外推有效。
- 适用于复杂函数逼近和抗噪反演，适合高精度物理模拟场景。
物理信息神经网络（PINNs）为模拟物理系统提供了有前景的方法，但其应用受限于优化难题，主要源于缺乏能在多种物理系统间良好泛化的激活函数。现有激活函数往往缺乏灵活性与泛化能力。为此，本文提出有理指数激活函数（REAct），它是tanh的广义形式，包含四个可学习的形状参数。实验表明，REAct优于多种标准及基准激活函数，在热传导问题上均方误差（MSE）比tanh低三个数量级，并能有效推广至训练域外更细网格和点。它在函数逼近任务中表现优异，同时提升了逆问题中的噪声鲁棒性，可在不同噪声水平下获得更准确的参数估计。
原文摘要 · Abstract (English)
Physics-Informed Neural Networks (PINNs) offer a promising approach to simulating physical systems. Still, their application is limited by optimization challenges, mainly due to the lack of activation functions that generalize well across several physical systems. Existing activation functions often lack such flexibility and generalization power. To address this issue, we introduce Rational Exponential Activation (REAct), a generalized form of tanh consisting of four learnable shape parameters. Experiments show that REAct outperforms many standard and benchmark activations, achieving an MSE three orders of magnitude lower than tanh on heat problems and generalizing well to finer grids and points beyond the training domain. It also excels at function approximation tasks and improves noise rejection in inverse problems, leading to more accurate parameter estimates across varying noise levels.
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