Sparsified time-dependent Fourier neural operators for fusion simulations

Rahman, Mustafa Mutiur; Bai, Zhe; King, Jacob Robert; Sovinec, Carl R.; Wei, Xishuo; Williams, Samuel; Liu, Yang

doi:10.1063/5.0232503

Sparsified time-dependent Fourier neural operators for fusion simulations

Journal Article · Wed Dec 04 00:00:00 EST 2024 · Physics of Plasmas

DOI:https://doi.org/10.1063/5.0232503· OSTI ID:2567804

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Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Fiat Lux, Lafayette, CO (United States)
University of Wisconsin, Madison, WI (United States)
University of California, Irvine, CA (United States)

This paper presents a sparsified Fourier neural operator for coupled time-dependent partial differential equations (ST-FNO) as an efficient machine learning surrogate for fluid and particle-based fusion codes such as NIMROD (Non-Ideal Magnetohydrodynamics with Rotation - Open Discussion) and GTC (Gyrokinetic Toroidal Code). ST-FNO leverages the structures in the governing equations and utilizes neural operators to represent Green's function-like numerical operators in the corresponding numerical solvers. Once trained, ST-FNO can rapidly and accurately predict dynamics in fusion devices compared with first-principle numerical algorithms. In general, ST-FNO represents an efficient and accurate machine learning surrogate for numerical simulators for multi-variable nonlinear time-dependent partial differential equations, with the proposed architectures and loss functions. The efficacy of ST-FNO has been demonstrated using quiescent H-mode simulation data from NIMROD and kink-mode simulation data from GTC. The ST-FNO H-mode results show orders of magnitude reduction in memory and central processing unit usage in comparison with the numerical solvers in NIMROD when computing fields over a selected poloidal plane. The ST-FNO kink-mode results achieve a factor of 2 reduction in the number of parameters compared to baseline FNO models without accuracy loss.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)

Grant/Contract Number:: AC02-05CH11231; AC02-09CH11466

OSTI ID:: 2567804

Alternate ID(s):: OSTI ID: 2549294

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 12 Vol. 31; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (28)

A pseudospectral algorithm for three-dimensional magnetohydrodynamic simulation Schnack, D. D.; Baxter, D. C.; Caramana, E. J. Journal of Computational Physics, Vol. 55, Issue 3 https://doi.org/10.1016/0021-9991(84)90034-2	journal	September 1984
An Eulerian gyrokinetic-Maxwell solver Candy, J.; Waltz, R. E. Journal of Computational Physics, Vol. 186, Issue 2 https://doi.org/10.1016/S0021-9991(03)00079-2	journal	April 2003
Nonlinear magnetohydrodynamics simulation using high-order finite elements Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A. Journal of Computational Physics, Vol. 195, Issue 1 https://doi.org/10.1016/j.jcp.2003.10.004	journal	March 2004
Analysis of a mixed semi-implicit/implicit algorithm for low-frequency two-fluid plasma modeling Sovinec, C. R.; King, J. R. Journal of Computational Physics, Vol. 229, Issue 16 https://doi.org/10.1016/j.jcp.2010.04.022	journal	August 2010
The global version of the gyrokinetic turbulence code GENE Görler, T.; Lapillonne, X.; Brunner, S. Journal of Computational Physics, Vol. 230, Issue 18 https://doi.org/10.1016/j.jcp.2011.05.034	journal	August 2011
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations Raissi, M.; Perdikaris, P.; Karniadakis, G. E. Journal of Computational Physics, Vol. 378 https://doi.org/10.1016/j.jcp.2018.10.045	journal	February 2019
gLaSDI: Parametric physics-informed greedy latent space dynamics identification He, Xiaolong; Choi, Youngsoo; Fries, William D. Journal of Computational Physics, Vol. 489 https://doi.org/10.1016/j.jcp.2023.112267	journal	September 2023
Predicting disruptive instabilities in controlled fusion plasmas through deep learning Kates-Harbeck, Julian; Svyatkovskiy, Alexey; Tang, William Nature, Vol. 568, Issue 7753 https://doi.org/10.1038/s41586-019-1116-4	journal	April 2019
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators Lu, Lu; Jin, Pengzhan; Pang, Guofei Nature Machine Intelligence, Vol. 3, Issue 3 https://doi.org/10.1038/s42256-021-00302-5	journal	March 2021
Simulation of current-filament dynamics and relaxation in the Pegasus Spherical Tokamak O’Bryan, J. B.; Sovinec, C. R.; Bird, T. M. Physics of Plasmas, Vol. 19, Issue 8 https://doi.org/10.1063/1.4746089	journal	August 2012
Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry Schnack, D. D.; Cheng, J.; Barnes, D. C. Physics of Plasmas, Vol. 20, Issue 6 https://doi.org/10.1063/1.4811468	journal	June 2013
The impact of collisionality, FLR, and parallel closure effects on instabilities in the tokamak pedestal: Numerical studies with the NIMROD code King, J. R.; Pankin, A. Y.; Kruger, S. E. Physics of Plasmas, Vol. 23, Issue 6 https://doi.org/10.1063/1.4954302	journal	June 2016
MHD modeling of a DIII-D low-torque QH-mode discharge and comparison to observations King, J. R.; Kruger, S. E.; Burrell, K. H. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4977467	journal	May 2017
Gyrokinetic particle simulations of the effects of compressional magnetic perturbations on drift-Alfvenic instabilities in tokamaks Dong, Ge; Bao, Jian; Bhattacharjee, Amitava Physics of Plasmas, Vol. 24, Issue 8 https://doi.org/10.1063/1.4997788	journal	August 2017
GTC simulation of linear stability of tearing mode and a model magnetic island stabilization by ECCD in toroidal plasma Li, Jingchun; Xiao, Chijie; Lin, Zhihong Physics of Plasmas, Vol. 27, Issue 4 https://doi.org/10.1063/1.5111127	journal	April 2020
Growing neoclassical tearing modes seeded via transient-induced-multimode interactions Howell, E. C.; King, J. R.; Kruger, S. E. Physics of Plasmas, Vol. 29, Issue 2 https://doi.org/10.1063/5.0076253	journal	February 2022
MHD stability in X-point geometry: simulation of ELMs Huysmans, G. T. A.; Czarny, O. Nuclear Fusion, Vol. 47, Issue 7 https://doi.org/10.1088/0029-5515/47/7/016	journal	June 2007
Full-f gyrokinetic particle simulation of centrally heated global ITG turbulence from magnetic axis to edge pedestal top in a realistic tokamak geometry Ku, S.; Chang, C. S.; Diamond, P. H. Nuclear Fusion, Vol. 49, Issue 11 https://doi.org/10.1088/0029-5515/49/11/115021	journal	September 2009
Towards validated MHD modeling of edge harmonic oscillation in DIII-D QH-mode discharges Pankin, A. Y.; King, J. R.; Kruger, S. E. Nuclear Fusion, Vol. 60, Issue 9 https://doi.org/10.1088/1741-4326/ab9afe	journal	July 2020
The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas Hoelzl, Matthias; Huijsmans, Guido; Pamela, Stanislas Nuclear Fusion https://doi.org/10.1088/1741-4326/abf99f	journal	April 2021
Deep learning based surrogate models for first-principles global simulations of fusion plasmas Dong, G.; Wei, X.; Bao, J. Nuclear Fusion, Vol. 61, Issue 12 https://doi.org/10.1088/1741-4326/ac32f1	journal	November 2021
Reconstruction of tokamak plasma safety factor profile using deep learning Wei, Xishuo; Sun, Shuying; Tang, William Nuclear Fusion, Vol. 63, Issue 8 https://doi.org/10.1088/1741-4326/acdf00	journal	June 2023
On the potential of physics-informed neural networks to solve inverse problems in tokamaks Rossi, Riccardo; Gelfusa, Michela; Murari, Andrea Nuclear Fusion, Vol. 63, Issue 12 https://doi.org/10.1088/1741-4326/ad067c	journal	November 2023
Plasma surrogate modelling using Fourier neural operators Gopakumar, Vignesh; Pamela, Stanislas; Zanisi, Lorenzo Nuclear Fusion, Vol. 64, Issue 5 https://doi.org/10.1088/1741-4326/ad313a	journal	April 2024
The M3D- C ¹ approach to simulating 3D 2-fluid magnetohydrodynamics in magnetic fusion experiments Jardin, S. C.; Ferraro, N.; Luo, X. Journal of Physics: Conference Series, Vol. 125 https://doi.org/10.1088/1742-6596/125/1/012044	journal	July 2008
Magnetohydrodynamics with physics informed neural operators Rosofsky, Shawn G.; Huerta, E. A. Machine Learning: Science and Technology, Vol. 4, Issue 3 https://doi.org/10.1088/2632-2153/ace30a	journal	July 2023
Turbulent Transport Reduction by Zonal Flows: Massively Parallel Simulations Lin, Z. Science, Vol. 281, Issue 5384 https://doi.org/10.1126/science.281.5384.1835	journal	September 1998
Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver Li, Xiaoye S.; Lin, Paul; Liu, Yang ACM Transactions on Mathematical Software, Vol. 49, Issue 1 https://doi.org/10.1145/3577197	journal	March 2023

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