Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 447, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2021.110683
Keywords
Scientific machine learning; Distributed machine learning; Domain decomposition; PINNs; Multi-GPU computing
Funding
- OSD/AFOSR MURI Grant [FA9550-20-1-0358]
- DOE PhILMs project [DE-SC0019453]
- DARPA CompMods grant [HR00112090062]
- Office of Science of the U.S. Department of Energy [ENG120, DE-AC05-00OR22725]
Ask authors/readers for more resources
A distributed framework for physics-informed neural networks (PINNs) is developed based on conservative PINNs (cPINNs) and extended PINNs (XPINNs), utilizing domain decomposition in space and time-space. Performance comparisons show that cPINNs are more efficient in terms of communication cost, while XPINNs offer greater flexibility in handling various forward problems.
We develop 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. Here, we present a parallel algorithm for cPINNs and XPINNs constructed with a hybrid programming model described by MPI + X, where X is an element of {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. We compare the performance of distributed cPINNs and XPINNs for various forward problems, using both weak and strong scalings. Our 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. To this end, we also present 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. (C) 2021 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available