Neural Network Representation of Time Integrators
This work addresses the problem of error analysis in physics-based integrators for computational scientists, though it appears incremental as it applies existing methods to a new representation.
The authors constructed deep neural network architectures that exactly replicate explicit Runge-Kutta time integration schemes, eliminating the need for training by providing pre-defined weights and biases. This approach separates right-hand side approximation errors from time integration errors, as demonstrated with a mass-damper-stiffness example.
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, i.e., 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.