KAR-HNN, an HNN built from univariate KAN blocks, shows mixed accuracy gains but fails to consistently reduce energy drift versus MLP-HNN.
Complex Physics-Informed Neural Network
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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.
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Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks
KAR-HNN, an HNN built from univariate KAN blocks, shows mixed accuracy gains but fails to consistently reduce energy drift versus MLP-HNN.