Physics-Informed Neural Networks for Complex Eigenfrequency Identification and Mode Structure Reconstruction of the Ground-State ITG Branch

2026-08-03

AI Summary

This study addresses the challenge of jointly identifying the complex eigenfrequency and two-dimensional complex-valued mode structure of ion temperature gradient (ITG) drift waves in the pedestal region of tokamak H-mode plasmas, where high-frequency localized oscillations, strong coupling between real and imaginary components, and nonlinear interactions pose significant difficulties. To overcome these issues, the authors propose a physics-informed neural network (PINN) framework that integrates Fourier feature encoding, complex-valued neural networks, and a three-stage training strategy, enabling joint reconstruction of the fundamental ITG mode under sparse observational data and partial differential equation constraints. This work is the first to incorporate Fourier feature encoding into complex-valued PINNs, effectively decoupling the optimization of eigenfrequency and mode structure, substantially outperforming existing PINN baselines, and laying the groundwork for analyzing higher-order and multi-branch drift wave instabilities.

Abstract

Physics-informed neural networks (PINNs) combine sparse observations with physical equations, providing an important approach for modeling complex plasma processes and inferring unknown physical quantities. The steep-gradient pedestal of high-confinement-mode tokamaks is closely linked to plasma confinement and edge transport. Analyzing ion-temperature-gradient (ITG) drift waves in this region requires jointly identifying complex eigenfrequencies and reconstructing two-dimensional complex-valued mode fields. Localized high-frequency oscillations, strong real-imaginary coupling, and nonlinear coupling between the mode field and eigenfrequency challenge PINN representation and joint optimization. To address these challenges, we propose a physics-informed neural framework combining Fourier feature encoding, complex-valued feature propagation, and three-stage training. Under sparse observations and physical constraints, it jointly solves for the complex eigenfrequency and mode field of a representative ground-state ITG branch. Experiments show that the framework accurately recovers the target complex eigenfrequency and two-dimensional complex-valued mode field and outperforms representative PINN baselines. It also provides a basis for analyzing higher-order and multiple-branch drift-wave modes.

Problem

• complex eigenfrequency
• mode structure reconstruction
• ion-temperature-gradient (ITG) drift waves
• physics-informed neural networks
• tokamak pedestal

Innovation

• Physics-Informed Neural Networks
• Complex Eigenfrequency Identification
• Mode Structure Reconstruction
• Fourier Feature Encoding
• Complex-Valued Neural Networks