Banach-valued random feature models, including random single-hidden-layer networks, universally approximate elements of Bochner spaces over non-compact domains with explicit approximation rates.
Random neural networks for rough volatility
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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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Universal approximation property of Banach space-valued random feature models including random neural networks
Banach-valued random feature models, including random single-hidden-layer networks, universally approximate elements of Bochner spaces over non-compact domains with explicit approximation rates.
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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.