A single-layer PINN using the trainable Cauchy activation function matches or beats larger multi-layer PINN baselines on smooth analytic PDE benchmarks.
Model Comparisons: XNet Outperforms KAN
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abstract
In the fields of computational mathematics and artificial intelligence, the need for precise data modeling is crucial, especially for predictive machine learning tasks. This paper explores further XNet, a novel algorithm that employs the complex-valued Cauchy integral formula, offering a superior network architecture that surpasses traditional Multi-Layer Perceptrons (MLPs) and Kolmogorov-Arnold Networks (KANs). XNet significant improves speed and accuracy across various tasks in both low and high-dimensional spaces, redefining the scope of data-driven model development and providing substantial improvements over established time series models like LSTMs.
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Complex Physics-Informed Neural Network
A single-layer PINN using the trainable Cauchy activation function matches or beats larger multi-layer PINN baselines on smooth analytic PDE benchmarks.