Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC
Abstract
An encoder–decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker–Planck–Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the $$\ell _2$$ loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the ‘soft’ constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the particle density, momentum and energy for all species of the system are calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, of the order of $$10^{-4}$$ , which is low enough if the error is of random nature, but not if it is of drift nature in time steps. The run time for the current Picard iterative solver of the operator is $O(n^2)$$ , where $$n$$ is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since its training only scales as $$O(n)$ . A wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.
- Authors:
-
[1];
[2];
[3];
[2];
[3];
[2]
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Columbia Univ., New York, NY (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Workforce Development for Teachers and Scientists (WDTS); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1820174
- Alternate Identifier(s):
- OSTI ID: 1863753
- Grant/Contract Number:
- AC02-06CH11357; AC02-09CH11466; AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Plasma Physics
- Additional Journal Information:
- Journal Volume: 87; Journal Issue: 2; Journal ID: ISSN 0022-3778
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; fusion plasma; plasma simulation
Citation Formats
Miller, M. A., Churchill, R. M., Dener, A., Chang, C. S., Munson, T., and Hager, R. Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC. United States: N. p., 2021.
Web. doi:10.1017/s0022377821000155.
Miller, M. A., Churchill, R. M., Dener, A., Chang, C. S., Munson, T., & Hager, R. Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC. United States. https://doi.org/10.1017/s0022377821000155
Miller, M. A., Churchill, R. M., Dener, A., Chang, C. S., Munson, T., and Hager, R. Wed .
"Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC". United States. https://doi.org/10.1017/s0022377821000155. https://www.osti.gov/servlets/purl/1820174.
@article{osti_1820174,
title = {Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC},
author = {Miller, M. A. and Churchill, R. M. and Dener, A. and Chang, C. S. and Munson, T. and Hager, R.},
abstractNote = {An encoder–decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker–Planck–Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the $\ell _2$ loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the ‘soft’ constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the particle density, momentum and energy for all species of the system are calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, of the order of $10^{-4}$ , which is low enough if the error is of random nature, but not if it is of drift nature in time steps. The run time for the current Picard iterative solver of the operator is $O(n^2)$ , where $n$ is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since its training only scales as $O(n)$ . A wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.},
doi = {10.1017/s0022377821000155},
journal = {Journal of Plasma Physics},
number = 2,
volume = 87,
place = {United States},
year = {Wed Mar 24 00:00:00 EDT 2021},
month = {Wed Mar 24 00:00:00 EDT 2021}
}
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