Temperature Field Reconstruction of Tungsten Monoblock Divertor on EAST using Physics-aware Neural Operator Transformer

Accurate monitoring of the divertor temperature field is critical for the operational safety and longevity of fusion devices like the Experimental Advanced Superconducting Tokamak (EAST). Traditional numerical methods, such as the Finite Element Method (FEM), are highly accurate but computationally intensive, making them unsuitable for the real-time control and rapid prediction required in active fusion environments. This paper investigates whether a deep learning-based operator can provide a fast, generalizable, and physically consistent alternative for temperature field reconstruction.

The authors propose the Physics-aware Neural Operator Transformer (PNOT), a framework designed to map boundary heat-flux conditions and global operating parameters to the spatiotemporal temperature field. PNOT introduces several key innovations:

• Structured Boundary Representation: Instead of compressing boundary conditions into a single vector, the model uses a graph-based representation to preserve the spatial distribution of heat fluxes.
• Physics-Aware Attention: The model employs a soft-slicing mechanism to group query points based on shared physical states, allowing for efficient modeling of global dependencies.
• Heat Graph Propagation: A spatial KNN graph is used to explicitly model local heat diffusion dynamics between query points.
• Sobolev Regularization: The training objective includes a graph-based Sobolev loss that penalizes discrepancies in both temperature values and spatial gradients, ensuring the reconstructed fields are physically consistent and smooth.

Experimental results on a dataset of 710 finite-element simulations of the EAST divertor demonstrate that PNOT significantly outperforms existing state-of-the-art neural operator models. PNOT achieved the lowest reconstruction errors across all metrics (Rel L2, rRMSE, rMAE, and MAE). Ablation studies confirm that each component—boundary tokens, Sobolev loss, and the physical module—contributes to improved accuracy and physical fidelity. Furthermore, the model exhibits strong out-of-distribution generalization, maintaining high accuracy even under unseen heat-flux operating conditions.