Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.
arXiv:2101.08068 (2021)
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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.
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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Random Neural Network Expressivity for Non-Linear Partial Differential Equations
Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.
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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.