用复数激活函数提升物理信息神经网络精度，单层即可解高维难题。
Complex Physics-Informed Neural Network
- 引入受柯西积分定理启发的可学习复数激活函数
- 单隐层即实现精度提升一个数量级，优于传统PINN
- 适合求解高维复杂物理方程，尤其擅长高维问题
我们提出 compleX-PINN，一种新型物理信息神经网络架构，其激活函数基于柯西积分定理设计并可学习。通过优化激活参数，compleX-PINN仅需单个隐藏层即可实现高精度。实证表明，compleX-PINN能有效解决传统PINN难以应对的高维问题，其在复杂任务上的表现显著更优，精度常提升一个数量级。
原文摘要 · Abstract (English)
We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by the Cauchy integral theorem. By optimizing the activation parameters, compleX-PINN achieves high accuracy with just a single hidden layer. Empirically, we demonstrate that compleX-PINN solves high-dimensional problems that pose significant challenges for PINNs. Our results show that compleX-PINN consistently achieves substantially greater precision, often improving accuracy by an order of magnitude, on these complex tasks.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。