A discrete-time random feature method with IMEX-RK time stepping derives a global error estimate and achieves 10^{-6} relative L2 errors with third-order convergence on Allen-Cahn, Burgers, KdV, and Cahn-Hilliard equations.
An introduction to the finite element method, 1993
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TAE combines Tikhonov regularization with autoencoders and a data randomization strategy to learn forward and inverse surrogates from one sample, with linear error bounds and tests on heat inversion and Navier-Stokes reconstruction.
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A Discrete-Time Random Feature Method for Nonlinear Evolution Equations with Implicit-Explicit Runge--Kutta Time Stepping
A discrete-time random feature method with IMEX-RK time stepping derives a global error estimate and achieves 10^{-6} relative L2 errors with third-order convergence on Allen-Cahn, Burgers, KdV, and Cahn-Hilliard equations.
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TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problems
TAE combines Tikhonov regularization with autoencoders and a data randomization strategy to learn forward and inverse surrogates from one sample, with linear error bounds and tests on heat inversion and Navier-Stokes reconstruction.