Investigating physics-informed neural networks for heat flux estimation: a sensitivity analysis towards Wendelstein 7-X applications

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Abstract Real-time estimation of divertor heat loads is critical for plasma-facing component protection in Wendelstein 7-X (W7-X). The current heat-flux reconstruction tool, THEODOR, is too computationally demanding for real-time use, motivating the development of faster physics-based surrogates. Physics-informed neural networks (PINNs) have recently been shown to model the heat equation and the associated heat-flux partial differential equation, though only for fixed boundary and initial conditions, when the heat potential profile at the top of the tile is represented as a Gaussian function. This choice is motivated by the observation that experimental profiles can be well approximated by a small number of Gaussian peaks in the strike-line region. Within this framework, the present work extends the PINN framework by assessing the sensitivity of the PDE solution to variations in the boundary and initial conditions, using a synthetic dataset with Gaussian boundary-condition profiles. Two approaches are investigated: (i) training multiple PINNs for different initial tile temperatures and Gaussian boundary-condition parameters; (ii) developing a parameterized PINN capable of solving the PDE across a continuous range of conditions. This approach demonstrates the feasibility of PINN-based heat-flux reconstruction with improved flexibility, in view of the application with real-time experimental data at W7-X.

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