Parallel Physics-informed Neural Networks via Domain Decomposition

January 25, 2023

1:00 pm – 2:00 pm Eastern time

Join us for this webinar describing parallel algorithms for cPINNs and XPINNs.

Khemraj Shukla and George Em Karniadakis
Division of Applied Mathematics, Brown University
Speaker: Khemraj Shukla

A research team at Brown University developed a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. During this webinar, the team will present a parallel algorithm for cPINNs and XPINNs constructed with a hybrid programming model described by MPI + X, where X ∈{CPUs ,GPUs}. The main advantage of cPINN and XPINN over the more classical data and model parallel approaches is the flexibility of optimizing all hyperparameters of each neural network separately in each subdomain. The team compared the performance of distributed cPINNs and XPINNs for various forward problems, using both weak and strong scalings. The results indicate that for space domain decomposition, cPINNs are more efficient in terms of communication cost but XPINNs provide greater flexibility, as they can also handle time-domain decomposition for any differential equations, and can deal with any arbitrarily shaped complex subdomains. The webinar will also feature an application of the parallel XPINN method for solving an inverse diffusion problem with variable conductivity on the United States map, using ten regions as subdomains.