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A Fourier neural operator (FNO) is one of the physics-inspired machine learning methods.
A theory of the learnable
L.G. Valiant · 1984
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Vc dimension of neural networks
E.D. Sontag · 1998
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An overview of statistical learning theory
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Understanding Machine Learning: From Theory to Algorithms
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Norm-based capacity control in neural networks
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A vector-contraction inequality for rademacher complexities
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Theoretical investigation of generalization bound for residual networks
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Generalization Error in Deep Learning
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Data-dependent generalization bounds for multi-class classification
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Fisher-rao metric, geometry, and complexity of neural networks
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Neural operator: Graph kernel network for partial differential equations
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Fourier neural operator for parametric partial differential equations
Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2021
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Learning nonlinear operators via deeponet based on the universal approximation theorem of operators
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Generalization bounds for graph convolutional neural networks via rademacher complexity
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Relative flatness and generalization
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