3 citations · 11 across the 13 of their papers we have counts for
5 papers · 1 filter
Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion
Ariel Neufeld, Philipp Schmocker
In this paper, we solve stochastic partial differential equations (SPDEs) numerically by using (possibly random) neural networks in the truncated Wiener chaos expansion of their co…
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains
Ariel Neufeld, Philipp Schmocker
This paper extends the universal approximation property of single-hidden-layer feedforward neural networks beyond compact domains, which is of particular interest for the approxima…
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in -sense
Ariel Neufeld, Tuan Anh Nguyen
We prove that multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation are capable of approximating solutions of semilinear Kolmogor…
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs
Ariel Neufeld, Philipp Schmocker, Sizhou Wu
In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks s…
Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations
Ariel Neufeld, Tuan Anh Nguyen
Numerical experiments indicate that deep learning algorithms overcome the curse of dimensionality when approximating solutions of semilinear PDEs. For certain linear PDEs and semil…