A Data-Free, Physics-Informed Surrogate Solver for Drift Kinetic Equation: Enabling Fast Neoclassical Toroidal Viscosity Torque Modeling in Tokamaks

Jinpeng Huang; Nana Bao; Weiyong Zhou; Xingting Yan; Youwen Sun; Yuetao Meng

arxiv: 2604.13447 · v1 · submitted 2026-04-15 · ⚛️ physics.plasm-ph

A Data-Free, Physics-Informed Surrogate Solver for Drift Kinetic Equation: Enabling Fast Neoclassical Toroidal Viscosity Torque Modeling in Tokamaks

Xingting Yan , Yuetao Meng , Nana Bao , Youwen Sun , Weiyong Zhou , Jinpeng Huang This is my paper

Pith reviewed 2026-05-10 12:50 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph

keywords drift kinetic equationphysics-informed neural networkneoclassical toroidal viscositytokamak plasmadata-free surrogatetoroidal rotationplasma transportsurrogate modeling

0 comments

The pith

A neural network trained only on the physical equations of the drift kinetic equation delivers accurate solutions without any simulation data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a surrogate model for solving the drift kinetic equation that relies solely on embedding the governing physical equations into the network's loss function and hard-coding the boundary conditions into the architecture. This data-free approach targets the computation of neoclassical toroidal viscosity torque induced by three-dimensional magnetic perturbations in tokamak plasmas, where traditional first-principle solvers are too slow for real-time applications like active control or integrated modeling. Validation against reference numerical solutions shows that the resulting predictions match the expected distribution function while reducing computation time substantially. The physics-driven surrogate also exhibits greater consistency with the underlying equations than comparable models trained on external datasets.

Core claim

The central claim is that a physics-informed neural network can serve as a data-free surrogate solver for the drift kinetic equation. Training minimizes the residual of the governing equations in the loss while the boundary conditions are incorporated directly into the model structure. When compared to solutions from conventional numerical methods, the network produces accurate results at significantly lower computational cost. The approach further demonstrates superior physical consistency relative to data-driven neural surrogates trained on the same problem.

What carries the argument

A physics-informed neural network that incorporates the residuals of the drift kinetic equation directly into its loss function and embeds the boundary conditions into the model architecture.

If this is right

Neoclassical toroidal viscosity torque can be evaluated fast enough for real-time feedback control in tokamak devices.
Integrated plasma modeling frameworks can incorporate NTV effects without the previous computational bottleneck.
Similar data-free surrogates become feasible for other high-dimensional kinetic equations where generating training data is expensive.
Purely physics-constrained networks can accelerate demanding computations across plasma transport problems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could extend to time-evolving or nonlinear versions of the drift kinetic equation for dynamic plasma scenarios.
Higher physical consistency may support reliable predictions outside the range of previously simulated cases.
Coupling the surrogate with optimization routines could enable rapid design of magnetic perturbations to achieve target torque profiles.

Load-bearing premise

The governing equations of the drift kinetic equation together with the boundary conditions are sufficient to determine the unique physical solution, and the neural network can represent that solution accurately when trained only on the equation residuals.

What would settle it

A test case in which the neural-network solution produces residuals of the drift kinetic equation that exceed the tolerance of the reference numerical solver or deviates measurably from the first-principle solution on a new set of magnetic-perturbation amplitudes or plasma parameters.

Figures

Figures reproduced from arXiv: 2604.13447 by Jinpeng Huang, Nana Bao, Weiyong Zhou, Xingting Yan, Youwen Sun, Yuetao Meng.

**Figure 1.** Figure 1: Key ideas and results of this paper. 2 Drift kinetic equation and NTV torque The drift kinetic equation in NTV torque modeling is a complexvalued ordinary differential equation, defined on the pitch angle variant coordinate [15]: 𝜅 2 ≜ 𝑣 2 /2 − 𝜇𝐵𝑚 𝜇(𝐵𝑀 − 𝐵𝑚) ∈ [0, 1], (1) where 𝑣 is the particle velocity, 𝜇 is the magnetic moment, 𝐵𝑀 and 𝐵𝑚 are the maximum and minimum magnetic field strength on one flux … view at source ↗

**Figure 2.** Figure 2: Evolution of (a) MSE and (b) 𝑅 2 on validation set during model training for three surrogates: 𝐷𝐾𝐸𝑑𝑎𝑡𝑎, 𝐷𝐾𝐸𝑝ℎ𝑦𝑠 and 𝐷𝐾𝐸𝑝ℎ𝑦𝑠,𝑏𝑐1. In addition to the standard evaluation metrics like MSE and 𝑅 2 , the relative prediction error 𝜀𝑠 is also defined to measure model accuracy for each single data sample: 𝜀𝑠 = |𝑓 − ˆ 𝑓 | max(|𝑓 |), (28) where 𝑓 and ˆ 𝑓 are ground truth and model prediction respectively, ’max’ oper… view at source ↗

**Figure 3.** Figure 3: Evolution of different components of physical loss [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 5.** Figure 5: Prediction of DKE solution (left column for [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 4.** Figure 4: Prediction of DKE solution (left column for [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: Comparison of calculation time between numerical [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

read the original abstract

Toroidal rotation is crucial for maintaining stable and high performance plasmas in tokamak fusion reactors. Among its driving mechanisms, the neoclassical toroidal viscosity (NTV) torque--induced by three-dimensional magnetic perturbations--is particularly significant due to its strong impact and controllability, especially for reactor-scale devices like ITER where conventional momentum injection method becomes less effective. However, traditional first-principle NTV modeling is computationally expensive, as it requires solving the drift kinetic equation (DKE) in high-dimensional phase space, therefore precluding any real-time applications such as active control or nonlinear integrated modeling of tokamak plasma. Although surrogate solver shows promising ability for accelerating scientific computations, obtaining the data required to train such model is still very challenging. In this work, we present a novel, data-free approach for developing fast surrogate solver of DKE, by training neural network solely based on physical constraints. Such physical constraints are implemented in two ways: First, the loss function is defined based on physical governing equations; Second, the boundary condition is hard-coded into the predicting model. The proposed model is validated against the dataset generated by first-principle numerical solver, which is found to achieve accurate DKE solution with significantly reduced time consuming. In particular, physics-driven surrogate shows higher physical consistency than data-driven surrogate. In general, our study provides a new idea for developing surrogate solvers in data-scarce scenarios, and demonstrates the potential of purely physics-driven neural networks to accelerate demanding scientific computations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper applies a data-free PINN to the drift kinetic equation for NTV torque with hard-coded boundaries, but the validation leaves the uniqueness and accuracy claims under-supported.

read the letter

The core idea here is a neural network trained only on the drift kinetic equation residual plus hard-coded boundary conditions to approximate the distribution function for neoclassical toroidal viscosity calculations. No training data from solvers is used, which addresses a real bottleneck in high-dimensional tokamak modeling where generating datasets is expensive. That part is straightforward and practical for people who need faster torque estimates in integrated simulations or real-time control loops. The comparison to a data-driven surrogate showing better physical consistency is also a useful point, as it highlights why embedding the collision operator and geometry terms directly in the loss can help avoid unphysical artifacts. The speed-up claim is plausible given how expensive full 5D DKE solves are. The soft spot is that the central claim of accuracy and physical correctness rests on post-training comparison to a first-principles solver without enough quantitative detail in the abstract or methods to judge how close the match actually is or whether the optimizer consistently reaches the physical solution rather than a nearby minimum. The loss landscape for an integro-differential equation like this can admit small perturbations that preserve low-order moments but change the torque, and nothing in the write-up rules that out with a uniqueness argument or systematic checks on the velocity-space integrals. Minor issues like missing error bars or dataset sizes compound that. This is worth sending to referees for plasma modeling groups who work on surrogate methods or NTV in ITER-relevant regimes. The problem is timely and the approach is a clean extension of existing PINN ideas, even if it will need tighter numerical evidence and perhaps some additional constraints to strengthen the results. I would bring it to a reading group for discussion on the loss design.

Referee Report

3 major / 3 minor

Summary. The paper introduces a data-free physics-informed neural network surrogate solver for the drift kinetic equation (DKE) to model neoclassical toroidal viscosity (NTV) torque in tokamaks. The method trains the network using a loss function derived from the DKE governing equations and incorporates hard-coded boundary conditions, eliminating the need for training data from numerical solvers. Validation is claimed against first-principle solvers, showing accurate solutions with reduced computation time and better physical consistency than data-driven approaches.

Significance. If the approach proves robust, it would represent a significant advancement in computational plasma physics by enabling rapid, physics-consistent solutions to high-dimensional kinetic equations without the prohibitive cost of generating large training datasets. This could facilitate real-time NTV torque calculations in tokamak control systems and nonlinear integrated modeling, which is particularly relevant for ITER and future fusion reactors where traditional methods are too slow. The data-free nature addresses a key limitation in surrogate modeling for data-scarce scientific problems and may have broader applicability to other integro-differential equations in the field.

major comments (3)

[Abstract] Abstract: The validation claim that the model achieves 'accurate DKE solution with significantly reduced time consuming' lacks any supporting quantitative metrics, such as error norms, relative errors, or specific timing comparisons. This undermines the ability to evaluate the central claim of accuracy and efficiency.
[Results and validation] Results and validation: The statement that the physics-driven surrogate 'shows higher physical consistency than data-driven surrogate' is presented without specific evidence or metrics demonstrating this consistency (e.g., errors in conserved quantities or NTV torque values). A direct comparison table or figure with quantitative data is needed to support this.
[Method (physics loss and boundary conditions)] Method (physics loss and boundary conditions): There is no analysis or proof demonstrating that minimizing the DKE residual loss with hard-coded BCs converges to the unique physical solution in the 5D phase space, especially considering the integro-differential collision operator and potential for spurious minima in the optimization landscape that could affect the NTV torque prediction. This is a load-bearing issue for the data-free claim.

minor comments (3)

[Abstract] Grammatical issue: 'significantly reduced time consuming' should be rephrased to 'significantly reduced computational time' or 'significantly lower time consumption'.
[Throughout] The dimensionality of the DKE (typically 5D: 3D space + 2D velocity) should be explicitly stated when discussing the phase space to clarify the computational challenge.
[References] Additional citations to existing physics-informed neural network applications in plasma physics or kinetic theory would help contextualize the novelty.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We have carefully considered each major comment and provide point-by-point responses below, along with our plans for revision.

read point-by-point responses

Referee: [Abstract] Abstract: The validation claim that the model achieves 'accurate DKE solution with significantly reduced time consuming' lacks any supporting quantitative metrics, such as error norms, relative errors, or specific timing comparisons. This undermines the ability to evaluate the central claim of accuracy and efficiency.

Authors: We agree with the referee that the abstract would be strengthened by the inclusion of quantitative metrics. Although the results section of the manuscript contains detailed comparisons, we will revise the abstract to explicitly state key performance metrics, including the relative error in the distribution function and the reduction in computational time, to better substantiate our claims of accuracy and efficiency. revision: yes
Referee: [Results and validation] Results and validation: The statement that the physics-driven surrogate 'shows higher physical consistency than data-driven surrogate' is presented without specific evidence or metrics demonstrating this consistency (e.g., errors in conserved quantities or NTV torque values). A direct comparison table or figure with quantitative data is needed to support this.

Authors: We acknowledge that a more direct and quantitative comparison is necessary to support the claim of higher physical consistency. In the revised version, we will include a dedicated table or figure that compares the physics-driven and data-driven surrogates using metrics such as deviations in conserved quantities and computed NTV torque values, providing clear evidence for the improved consistency of the physics-informed approach. revision: yes
Referee: [Method (physics loss and boundary conditions)] Method (physics loss and boundary conditions): There is no analysis or proof demonstrating that minimizing the DKE residual loss with hard-coded BCs converges to the unique physical solution in the 5D phase space, especially considering the integro-differential collision operator and potential for spurious minima in the optimization landscape that could affect the NTV torque prediction. This is a load-bearing issue for the data-free claim.

Authors: We recognize the importance of addressing the theoretical foundations of our data-free method. While the current manuscript relies on empirical validation against first-principle solvers to demonstrate that the solutions are physically relevant, we agree that additional analysis is warranted. We will add a discussion in the methods section on the properties of the physics loss function, the role of hard-coded boundary conditions, and numerical studies exploring the optimization landscape to reduce concerns about spurious minima. However, providing a complete mathematical proof of convergence and uniqueness for this high-dimensional integro-differential problem is beyond the scope of the present work. revision: partial

standing simulated objections not resolved

A rigorous proof demonstrating convergence to the unique physical solution in the 5D phase space

Circularity Check

0 steps flagged

No significant circularity; method implements external physical laws with independent validation

full rationale

The paper trains a neural network by minimizing a loss constructed directly from the drift kinetic equation residuals plus hard-coded boundary conditions, with no training data or fitted parameters from the target outputs. Validation occurs against an external first-principle numerical solver that generates independent reference solutions, rather than any self-referential or constructed equivalence. No self-citations are invoked to justify uniqueness or load-bearing premises, no ansatzes are smuggled, and no known results are renamed as novel derivations. The central claim therefore reduces to the standard PINN procedure of enforcing known governing equations, which is self-contained against external benchmarks and does not collapse to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the standard drift kinetic equation as the complete physical model and the assumption that a neural network can be trained to satisfy it via residual minimization without data.

free parameters (1)

Neural network architecture and hyperparameters
Layers, neurons, activation functions, and loss weighting coefficients are chosen to minimize the physics residual; specific values not provided.

axioms (1)

domain assumption The drift kinetic equation governs the plasma distribution function relevant to neoclassical toroidal viscosity torque.
Invoked as the sole governing equation implemented in the loss function.

pith-pipeline@v0.9.0 · 5596 in / 1321 out tokens · 59116 ms · 2026-05-10T12:50:15.586593+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

[1]

M Bécoulet, M Kim, G Yun, S Pamela, J Morales, X Garbet, G T A Huijsmans, C Passeron, O Février, M Hoelzl, A Lessig, and F Orain. 2017. Non-linear MHD modelling of edge localized modes dynamics in KSTAR.Nuclear Fusion57, 11 (Aug. 2017), 116059

work page 2017
[2]

Woojin Cho, Minju Jo, Haksoo Lim, Kookjin Lee, Dongeun Lee, Sanghyun Hong, and Noseong Park. 2024. Parameterized physics-informed neural networks for parameterized PDEs. InProceedings of the 41st International Conference on Machine Learning (ICML’24). JMLR.org. Place: Vienna, Austria

work page 2024
[3]

M D Clement, N C Logan, and M D Boyer. 2021. Neoclassical toroidal viscosity torque prediction via deep learning.Nuclear Fusion62, 2 (Dec. 2021), 26022

work page 2021
[4]

Salvatore Cuomo, Vincenzo Schiano Di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, and Francesco Piccialli. 2022. Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next.Journal of Scientific Computing92, 3 (July 2022), 88

work page 2022
[5]

Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. 2016. Deep Residual Learning for Image Recognition. In2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 770–778

work page 2016
[6]

Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang

George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. 2021. Physics-informed machine learning.Nature Reviews Physics3, 6 (June 2021), 422–440

work page 2021
[7]

S. K. Kim, R. Shousha, S. M. Yang, Q. Hu, S. H. Hahn, A. Jalalvand, J.-K. Park, N. C. Logan, A. O. Nelson, Y.-S. Na, R. Nazikian, R. Wilcox, R. Hong, T. Rhodes, C. Paz-Soldan, Y. M. Jeon, M. W. Kim, W. H. Ko, J. H. Lee, A. Battey, G. Yu, A. Bortolon, J. Snipes, and E. Kolemen. 2024. Highest fusion performance without harmful edge energy bursts in tokamak....

work page 2024
[8]

A Loarte, R A Pitts, T Wauters, I Nunes, P de Vries, S H Kim, F Köchl, A Polevoi, M Lehnen, J Artola, S Jachmich, A Pshenov, X Bai, I S Carvalho, M Dubrov, Y Gribov, M Schneider, L Zabeo, X Bonnin, S D Pinches, F Poli, G Suarez Lopez, M Merola, F Escourbiac, R Hunt, L Chen, D Boilson, P Veltri, N Casal, M Preynas, A Mukherjee, W Helou, F Kazarian, S Willm...

work page 2025
[9]

N. C. Logan, Q. Hu, C. Paz-Soldan, R. Nazikian, T. Rhodes, T. Wilks, S. Munaretto, A. Bortolon, F. Laggner, F. Scotti, R. Hong, and H. Wang. 2022. Improved Particle Confinement with Resonant Magnetic Perturbations in DIII-D Tokamak H-Mode Plasmas.Phys. Rev. Lett.129, 20 (Nov. 2022), 205001

work page 2022
[10]

Park, S M Yang, and Q Hu

N C Logan, C Zhu, J.-K. Park, S M Yang, and Q Hu. 2021. Physics basis for design of 3D coils in tokamaks.Nuclear Fusion61, 7 (June 2021), 76010

work page 2021
[11]

Jong-Kyu Park, Allen H Boozer, and Jonathan E Menard. 2009. Nonambipolar Transport by Trapped Particles in Tokamaks.Physical Review Letters102 (2 2009), 65002. Issue 6

work page 2009
[12]

Raissi, P

M. Raissi, P. Perdikaris, and G. E. Karniadakis. 2019. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.J. Comput. Phys.378 (2019), 686–707. A Data-Free, Physics-Informed Surrogate Solver for Drift Kinetic Equation: Enabling Fast Neoclassical Toroidal Vi...

work page 2019
[13]

K C Shaing. 2003. Magnetohydrodynamic-activity-induced toroidal momentum dissipation in collisionless regimes in tokamaks.Physics of Plasmas10 (2003), 1443–1448. Issue 5

work page 2003
[14]

K C Shaing, K Ida, and S A Sabbagh. 2015. Neoclassical plasma viscosity and transport processes in non-axisymmetric tori.Nuclear Fusion55 (11 2015), 125001. Issue 12

work page 2015
[15]

Y Sun, X Li, K He, and K C Shaing. 2019. Unified modeling of both resonant and non-resonant neoclassical transport under non-axisymmetric magnetic perturba- tions in tokamaks.Physics of Plasmas26 (2019), 72504. Issue 7

work page 2019
[16]

Y. Sun, Y. Liang, K.C. Shaing, H.R. Koslowski, C. Wiegmann, and T. Zhang

work page
[17]

Nuclear Fusion51, 5 (April 2011), 053015

Modelling of the neoclassical toroidal plasma viscosity torque in tokamaks. Nuclear Fusion51, 5 (April 2011), 053015

work page 2011
[18]

Y. Sun, Y. Liang, K. C. Shaing, H. R. Koslowski, C. Wiegmann, and T. Zhang

work page
[19]

2010), 145002

Neoclassical Toroidal Plasma Viscosity Torque in Collisionless Regimes in Tokamaks.Physical Review Letters105, 14 (Oct. 2010), 145002

work page 2010
[20]

B N Wan, Y F Liang, X Z Gong, J G Li, N Xiang, G S Xu, Y W Sun, L Wang, J P Qian, H Q Liu, X D Zhang, L Q Hu, J S Hu, F K Liu, C D Hu, Y P Zhao, L Zeng, M Wang, H D Xu, G N Luo, A M Garofalo, A Ekedahl, L Zhang, X J Zhang, J Huang, B J Ding, Q Zang, M H Li, F Ding, S Y Ding, B Lyu, Y W Yu, T Zhang, Y Zhang, G Q Li, T Y Xia, the EAST team, and Collaborator...

work page 2017
[21]

X.M. Wu, Y. Sun, Q. Ma, S. Gu, Y.F. Wang, K.N. Geng, X.X. Zhang, G.Q. Li, H. Sheng, T. Zhang, P.B. Snyder, Q. Zhang, J. qian, Y.Y. Li, and B. Wan. 2025. Influence of n = 4 RMPs on pedestal structure and stability in EAST.Nuclear Fusion65, 7 (June 2025), 076031

work page 2025
[22]

Yan, N.-N

X.-T. Yan, N.-N. Bao, C.-Y. Zhao, Y.-W. Sun, Y.-T. Meng, W.-Y. Zhou, N.-Y. Liang, Y.-X. Lu, Y.-F. Liang, and B.-N. Wan. 2025. NTVTOK-ML: Fast surrogate model for neoclassical toroidal viscosity torque calculation in tokamaks based on machine learning methods.Computer Physics Communications307 (Feb. 2025), 109413

work page 2025
[23]

Park, Yong-Su Na, Z R Wang, W H Ko, Y In, J H Lee, K D Lee, and S K Kim

S M Yang, J.-K. Park, Yong-Su Na, Z R Wang, W H Ko, Y In, J H Lee, K D Lee, and S K Kim. 2019. Nonambipolar Transport due to Electrons with 3D Resistive Response in the KSTAR Tokamak.Physical Review Letters123 (8 2019), 95001. Issue 9

work page 2019

[1] [1]

M Bécoulet, M Kim, G Yun, S Pamela, J Morales, X Garbet, G T A Huijsmans, C Passeron, O Février, M Hoelzl, A Lessig, and F Orain. 2017. Non-linear MHD modelling of edge localized modes dynamics in KSTAR.Nuclear Fusion57, 11 (Aug. 2017), 116059

work page 2017

[2] [2]

Woojin Cho, Minju Jo, Haksoo Lim, Kookjin Lee, Dongeun Lee, Sanghyun Hong, and Noseong Park. 2024. Parameterized physics-informed neural networks for parameterized PDEs. InProceedings of the 41st International Conference on Machine Learning (ICML’24). JMLR.org. Place: Vienna, Austria

work page 2024

[3] [3]

M D Clement, N C Logan, and M D Boyer. 2021. Neoclassical toroidal viscosity torque prediction via deep learning.Nuclear Fusion62, 2 (Dec. 2021), 26022

work page 2021

[4] [4]

Salvatore Cuomo, Vincenzo Schiano Di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, and Francesco Piccialli. 2022. Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next.Journal of Scientific Computing92, 3 (July 2022), 88

work page 2022

[5] [5]

Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. 2016. Deep Residual Learning for Image Recognition. In2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 770–778

work page 2016

[6] [6]

Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang

George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. 2021. Physics-informed machine learning.Nature Reviews Physics3, 6 (June 2021), 422–440

work page 2021

[7] [7]

S. K. Kim, R. Shousha, S. M. Yang, Q. Hu, S. H. Hahn, A. Jalalvand, J.-K. Park, N. C. Logan, A. O. Nelson, Y.-S. Na, R. Nazikian, R. Wilcox, R. Hong, T. Rhodes, C. Paz-Soldan, Y. M. Jeon, M. W. Kim, W. H. Ko, J. H. Lee, A. Battey, G. Yu, A. Bortolon, J. Snipes, and E. Kolemen. 2024. Highest fusion performance without harmful edge energy bursts in tokamak....

work page 2024

[8] [8]

A Loarte, R A Pitts, T Wauters, I Nunes, P de Vries, S H Kim, F Köchl, A Polevoi, M Lehnen, J Artola, S Jachmich, A Pshenov, X Bai, I S Carvalho, M Dubrov, Y Gribov, M Schneider, L Zabeo, X Bonnin, S D Pinches, F Poli, G Suarez Lopez, M Merola, F Escourbiac, R Hunt, L Chen, D Boilson, P Veltri, N Casal, M Preynas, A Mukherjee, W Helou, F Kazarian, S Willm...

work page 2025

[9] [9]

N. C. Logan, Q. Hu, C. Paz-Soldan, R. Nazikian, T. Rhodes, T. Wilks, S. Munaretto, A. Bortolon, F. Laggner, F. Scotti, R. Hong, and H. Wang. 2022. Improved Particle Confinement with Resonant Magnetic Perturbations in DIII-D Tokamak H-Mode Plasmas.Phys. Rev. Lett.129, 20 (Nov. 2022), 205001

work page 2022

[10] [10]

Park, S M Yang, and Q Hu

N C Logan, C Zhu, J.-K. Park, S M Yang, and Q Hu. 2021. Physics basis for design of 3D coils in tokamaks.Nuclear Fusion61, 7 (June 2021), 76010

work page 2021

[11] [11]

Jong-Kyu Park, Allen H Boozer, and Jonathan E Menard. 2009. Nonambipolar Transport by Trapped Particles in Tokamaks.Physical Review Letters102 (2 2009), 65002. Issue 6

work page 2009

[12] [12]

Raissi, P

M. Raissi, P. Perdikaris, and G. E. Karniadakis. 2019. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.J. Comput. Phys.378 (2019), 686–707. A Data-Free, Physics-Informed Surrogate Solver for Drift Kinetic Equation: Enabling Fast Neoclassical Toroidal Vi...

work page 2019

[13] [13]

K C Shaing. 2003. Magnetohydrodynamic-activity-induced toroidal momentum dissipation in collisionless regimes in tokamaks.Physics of Plasmas10 (2003), 1443–1448. Issue 5

work page 2003

[14] [14]

K C Shaing, K Ida, and S A Sabbagh. 2015. Neoclassical plasma viscosity and transport processes in non-axisymmetric tori.Nuclear Fusion55 (11 2015), 125001. Issue 12

work page 2015

[15] [15]

Y Sun, X Li, K He, and K C Shaing. 2019. Unified modeling of both resonant and non-resonant neoclassical transport under non-axisymmetric magnetic perturba- tions in tokamaks.Physics of Plasmas26 (2019), 72504. Issue 7

work page 2019

[16] [16]

Y. Sun, Y. Liang, K.C. Shaing, H.R. Koslowski, C. Wiegmann, and T. Zhang

work page

[17] [17]

Nuclear Fusion51, 5 (April 2011), 053015

Modelling of the neoclassical toroidal plasma viscosity torque in tokamaks. Nuclear Fusion51, 5 (April 2011), 053015

work page 2011

[18] [18]

Y. Sun, Y. Liang, K. C. Shaing, H. R. Koslowski, C. Wiegmann, and T. Zhang

work page

[19] [19]

2010), 145002

Neoclassical Toroidal Plasma Viscosity Torque in Collisionless Regimes in Tokamaks.Physical Review Letters105, 14 (Oct. 2010), 145002

work page 2010

[20] [20]

B N Wan, Y F Liang, X Z Gong, J G Li, N Xiang, G S Xu, Y W Sun, L Wang, J P Qian, H Q Liu, X D Zhang, L Q Hu, J S Hu, F K Liu, C D Hu, Y P Zhao, L Zeng, M Wang, H D Xu, G N Luo, A M Garofalo, A Ekedahl, L Zhang, X J Zhang, J Huang, B J Ding, Q Zang, M H Li, F Ding, S Y Ding, B Lyu, Y W Yu, T Zhang, Y Zhang, G Q Li, T Y Xia, the EAST team, and Collaborator...

work page 2017

[21] [21]

X.M. Wu, Y. Sun, Q. Ma, S. Gu, Y.F. Wang, K.N. Geng, X.X. Zhang, G.Q. Li, H. Sheng, T. Zhang, P.B. Snyder, Q. Zhang, J. qian, Y.Y. Li, and B. Wan. 2025. Influence of n = 4 RMPs on pedestal structure and stability in EAST.Nuclear Fusion65, 7 (June 2025), 076031

work page 2025

[22] [22]

Yan, N.-N

X.-T. Yan, N.-N. Bao, C.-Y. Zhao, Y.-W. Sun, Y.-T. Meng, W.-Y. Zhou, N.-Y. Liang, Y.-X. Lu, Y.-F. Liang, and B.-N. Wan. 2025. NTVTOK-ML: Fast surrogate model for neoclassical toroidal viscosity torque calculation in tokamaks based on machine learning methods.Computer Physics Communications307 (Feb. 2025), 109413

work page 2025

[23] [23]

Park, Yong-Su Na, Z R Wang, W H Ko, Y In, J H Lee, K D Lee, and S K Kim

S M Yang, J.-K. Park, Yong-Su Na, Z R Wang, W H Ko, Y In, J H Lee, K D Lee, and S K Kim. 2019. Nonambipolar Transport due to Electrons with 3D Resistive Response in the KSTAR Tokamak.Physical Review Letters123 (8 2019), 95001. Issue 9

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