Zhe Bai

A physics-constrained neural network is developed to predict radiated power across multiple plasma regions from foil bolometer measurements using a limited set of real-time equilibrium features. The surrogate model enforces a linear mapping between measured brightness and radiated power, enabling efficient inference with microsecond latency, suitable for real-time deployment. Model training is performed on a combination of large synthetic and real experimental datasets, allowing the neural network to learn the mapping between the measured signal and radiated power across varying plasma shapes while accounting for experimental noise, thereby improving its robustness. The model is optimized to estimate near-axis radiated power, enabling early detection of ongoing impurity accumulation. The approach has been implemented in the DIII-D plasma control system, demonstrating its capability for real-time operation.

In this work, we present the development of robust surrogate models for Ion Cyclotron Range of Frequencies (ICRF) and High-Harmonic Fast Wave (HHFW) heating predictions in fusion plasmas. Building upon our previous efforts to achieve real-time capable models, we identify the cause of the outliers found using TORIC in certain HHFW heating scenarios. The outliers are observed to be spurious ion Bernstein wave (IBW)-like modes caused by a wavelength control algorithm designed to address challenging scenarios with high perpendicular wavenumbers. The effect arises from the modulation in the perpendicular susceptibility, which can induce sign reversal and IBW-like propagation for scenarios featuring normalized ion Larmor radius λi≫1. We use TORIC with this algorithm disabled to generate a novel HHFW-NSTX database that is free of outliers. Surrogate models trained on this database, including Random Forest Regressor (RFR), Multi-Layer Perceptrons, and Gaussian Process Regressors (GPR), demonstrate the ability to accurately predict HHFW heating profiles, with regression scores of R2∈[0.93−0.99]. Additionally we demonstrate that it is possible to generalize predictions beyond training data by the use of both RFR and GPR models, enabling the prediction of scenarios previously limited to the original model. GPR models also provide uncertainty quantification, offering insights into model confidence. This work introduces a comprehensive Verification, Validation, and Uncertainty Quantification methodology for surrogate modeling, applicable not only to ICRF heating but also to other RF heating challenges and fusion physics problems. Beyond accelerated inference, these models show effective extrapolation capabilities, providing an alternative for addressing numerical challenges.

Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel, data-driven model reduction methods, coupled with detection of abnormal modes with plasma physics, opens a unique opportunity to identify plasma instabilities through automated construction of parsimonious models that can be tuned to balance accuracy and cost. Our fusion transfer learning (FTL) model demonstrates success in rapidly reconstructing nonlinear kink mode structures by learning from a limited amount of nonlinear simulation data. The knowledge transfer process leverages a pre-trained neural encoder–decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL’s capacity to capture transitional behaviors and dynamical features in plasma dynamics—a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics modes.

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.

A real-time capable core Ion Cyclotron Range of Frequencies (ICRF) heating model on NSTX and WEST is developed. The model is based on two nonlinear regression algorithms, the random forest ensemble of decision trees and the multilayer perceptron neural network. The algorithms are trained on TORIC ICRF spectrum solver simulations of the expected flat-top operation scenarios in NSTX and WEST assuming Maxwellian plasmas. The surrogate models are shown to successfully capture the multi-species core ICRF power absorption predicted by the original model for the high harmonic fast wave and the ion cyclotron minority heating schemes while reducing the computational time by six orders of magnitude. Although these models can be expanded, the achieved regression scoring, computational efficiency and increased model robustness suggest these strategies can be implemented into integrated modeling frameworks for real-time control applications.

Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma physics, opens a unique opportunity for building efficient models to identify plasma instabilities for real-time control. Our Fusion Transfer Learning (FTL) model demonstrates success in reconstructing nonlinear kink mode structures by learning from a limited amount of nonlinear simulation data. The knowledge transfer process leverages a pre-trained neural encoder-decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL’s capacity to capture transitional behaviors and dynamical features in plasma dynamics -- a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics (MHD) modes.