Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

DOI10.1007/s42985-023-00244-0arXiv2205.03672MaRDI QIDQ6204733

Benno Kuckuck, Loïc Pellissier, Victor Boussange, Sebastian Becker, Arnulf Jentzen

Publication date: 2 April 2024

Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.03672

zbMATH Keywords

PDEneural networksNeumann boundary conditionpartial differential equationreflected Brownian motionnon-localdeep learning

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Monte Carlo methods (65C05) Integro-partial differential equations (45K05) Initial-boundary value problems for second-order parabolic equations (35K20) Integro-partial differential equations (35R09) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Numerical analysis (65-XX) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

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