P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.
arXiv:2101.08068 (2021)
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ADANNs design ANN architectures and initializations to mimic classical numerical algorithms for parametric PDE operator approximation and report significant outperformance over existing methods in numerical tests.
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P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.
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Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
ADANNs design ANN architectures and initializations to mimic classical numerical algorithms for parametric PDE operator approximation and report significant outperformance over existing methods in numerical tests.