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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| Veröffentlicht in: | International journal for numerical methods in engineering 2023-09, Vol.124 (18), p.4192-4198 |
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| container_title | International journal for numerical methods in engineering |
| container_volume | 124 |
| creator | Löhner, Rainald Antil, Harbir |
| description | 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. |
| doi_str_mv | 10.1002/nme.7306 |
| format | Article |
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| subjects | Approximation Artificial neural networks deep neural networks Errors Integrators Mathematical analysis numerical integration Runge-Kutta method Runge–Kutta Time integration |
| title | Neural network representation of time integrators |
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