most citedDeep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the -sense

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cs.LG2024

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations

Julia Ackermann, Arnulf Jentzen, Benno Kuckuck +1

It is a challenging topic in applied mathematics to solve high-dimensional nonlinear partial differential equations (PDEs). Standard approximation methods for nonlinear PDEs suffer…

cs.LG2024

Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials

Shakil Rafi, Joshua Lee Padgett, Ukash Nakarmi

We make the case for neural network objects and extend an already existing neural network calculus explained in detail in Chapter 2 on \cite{bigbook}. Our aim will be to show that,…