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 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.

Automated summary

Deep neural network (DNN) architectures act as explicit Runge-Kutta schemes for numerical time integration without the need for training. The DNN approximation of the right-hand side is the only task left for physics-based integrators, allowing for clear estimation of approximation errors. An example of the architecture required for integrating a mass-damper-stiffness case is provided.