FTL: Transfer Learning Nonlinear Plasma Dynamic Transitions in Low Dimensional Embeddings via Deep Neural Networks

TL;DR

The paper addresses the challenge of representing and predicting high-dimensional, nonlinear plasma dynamics in tokamak devices. It introduces Fusion Transfer Learning (FTL), an encoder–decoder reduced-order model that maps plasma states to a low-dimensional latent space $\mathbf{Z}\in\mathbb{R}^d$ and enables real-time reconstruction, anomaly detection, and analysis of nonlinear bifurcations by transferring knowledge from linear kink simulations to nonlinear, kinetic regimes. Key contributions include a transferable ROM with an anomaly-filtering mechanism, demonstration of extrapolation to unseen nonlinear kink structures via transfer learning, and clear links between latent-space tipping points and physical-space/Fourier-domain transitions. The approach promises real-time plasma state assessment and has potential to inform control strategies in tokamaks, with extensions to other MHD modes and integration with physics-informed surrogates.

Abstract

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.

Figures (10)

• Figure 1: Schematic diagram of the FTL model using an encoder ($\Phi$) - decoder ($\Psi$) network. The coherent structure is compressed to a low-dimensional vector $\boldsymbol{Z}$ while the inherent dynamics are preserved in the latent space through embedding. Regularization is employed to impose penalties on the model's complexity. An anomaly filtering subroutine is utilized for the identification of outliers, thereby improving the fidelity of the pre-trained model.
• Figure 2: Comparison between the original and reconstructed kink modes for five samples from the test data. A larger reconstruction residual is observed for atypical mode structures.
• Figure 3: Detected anomalous modes using trained FTL network on the test set: (a) a histogram of sample density vs. normalized error highlighting anomalies in the tail of the distribution, (b) the original, reconstruction, and residual for five kink mode samples in the highlighted in the anomalous (shaded) region of (a), threshold parameter $\tau= 0.95$.
• Figure 4: (a) Simulated Kink modes with kinetic effects and reconstructed nonlinear mode structures at $t=0.073, 0.135, 0.186, 0.223, 0.250, 0.272, 0.295$ ms using the trained FTL model. (b) Training and validation error vs. epoch number. The solid lines are results averaged over using $20$ different random realizations. The shaded region indicates the distribution of the variance of the reconstruction error in the multiple runs. Early stopping (red dots) is used during the NN training to prevent overfitting.
• Figure 5: (a) Dynamics trajectory of the plasma state evolution in the latent space with time mapped as color. A bifurcation point is observed when the modes transit from linear to nonlinear. (b) latent space vector vs. time. (c) Correlation coefficient of reconstructed modes and ground truth over the time window, $\Delta t_s = 0.5 R_0/C_s = 1.483\mu s$.