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

TL;DR

This paper introduces a physics-informed, data-free neural network surrogate for solving the drift kinetic equation, enabling faster modeling of neoclassical toroidal viscosity torque in tokamaks.

Contribution

It presents a novel physics-driven neural network approach that does not require training data, improving computational efficiency and physical consistency in solving the drift kinetic equation.

Findings

Achieves accurate DKE solutions with reduced computational time.

Higher physical consistency than data-driven surrogates.

Validates against first-principle numerical solver data.

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.