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

1 citations · 1 across the 2 of their papers we have counts for

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2 papers

cs.LG2024★ 1 cited

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…

math.DS2024

Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems

Julia Ackermann, Matthias Ehrhardt, Thomas Kruse +1

This study revisits a recently proposed symmetric port-Hamiltonian single-file model in one dimension. The uniform streaming solutions are stable in the deterministic model. Howeve…