Parallel in time algorithms for multiscale dynamical systems using interpolation and neural networks
Gopal Yalla, Bjorn E. Engquist · High Performance Computing Symposium · 2018
The parareal algorithm allows for efficient parallel in time computation of dynamical systems. We present a novel coarse scale solver to be used in the parareal framework. The coarse scale solver can be defined through interpolation or as the output of a neural network, and accounts for slow scale motion in the system. Through a parareal scheme, we pair this coarse solver with a fine scale solver that corrects for fast scale motion. By doing so we are able to achieve the accuracy of the fine solver at the efficiency of the coarse solver. Successful tests for smaller but challenging problems are presented, which cover both highly oscillatory solutions and problems with strong forces localized in time. The results suggest significant speed up can be gained for multiscale problems when using a parareal scheme with this new coarse solver as opposed to the traditional parareal setup.