Neural network representation of time integrators

Deep neural network (DNN) architectures are constructed that are the exact equivalent of explicit Runge–Kutta schemes for numerical time integration. The network weights and biases are given, that is, no training is needed. In this way, the only task left for physics‐based integrators is the DNN app...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2023-09, Vol.124 (18), p.4192-4198
Main Authors: Löhner, Rainald, Antil, Harbir
Format: Article
Language:English
Subjects:
Approximation
Artificial neural networks
deep neural networks
Errors
Integrators
Mathematical analysis
numerical integration
Runge-Kutta method
Runge–Kutta
Time integration
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Description
Summary:Deep neural network (DNN) architectures are constructed that are the exact equivalent of explicit Runge–Kutta schemes for numerical time integration. The network weights and biases are given, that is, no training is needed. In this way, the only task left for physics‐based integrators is the DNN approximation of the right‐hand side. This allows to clearly delineate the approximation estimates for right‐hand side errors and time integration errors. The architecture required for the integration of a simple mass‐damper‐stiffness case is included as an example.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.7306