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

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 compu-
tationally demanding for real-time use, motivating the development of faster physics-based sur-
rogates. 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 bound-
ary 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)
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developing a parameterized PINN capable of solving the PDE across a continuous range of con-
ditions. 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