If you wish to access the seminar remotely, please use the following link:
Join Zoom Meeting: https://cwi-nl.zoom.us/j/83063963402?pwd=cWN3RjlEOVk1SkJIYWk2MEJmSzJMdz09
Meeting ID: 830 6396 3402
Passcode: 067208
Parallelization approaches for neural network-based collocation methods
Victorita Dolean
Eindhoven University of Technology
We consider neural network solvers for differential equation-based problems based on the pioneering collocation approach introduced by Lagaris et al. Those methods are very versatile as they may not require an explicit mesh, allow for the solution of parameter identification problems, and be well-suited for high- dimensional problems. However, the training of these neural network models is generally not very robust and may require a lot of hyper parameter tuning. In particular, due to the so-called spectral bias, the training is notoriously difficult when scaling up to large computational domains as well as for multiscale problems. In this work, we give an overview of the methods from the literature and we focus later on two overlapping domain decomposition-based techniques, namely finite basis physics-informed neural networks (FBPINNs) and deep do- main decomposition (Deep-DDM) methods. Whereas the former introduces the domain decomposition via a partition of unity within the classical gradient- based optimization, the latter employs a classical outer Schwarz iteration. In order to obtain scalability and robustness for multiscale problems, we consider a multi-level framework for both approaches.
