Differentiable sensor placement optimisation for aerodynamic wing pressure field reconstruction

  • Alfaro Moreno, Juan (INTA)
  • Castellanos García de Blas, Rodrigo (UC3M)
  • Sanmiguel Vila, Carlos (INTA)

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Accurate reconstruction of aerodynamic pressure fields from sparse measurements is a key enabling technology for data driven monitoring, digital twins and efficient reduced order modelling in aeronautics. This work investigates the application of a differentiable sensor placement framework coupled with deep learning for the reconstruction of surface pressure coefficient (Cp) fields over a realistic aircraft wing. Unlike post hoc optimal sensor placement strategies based on feature attribution, such as SHAP or saliency maps applied to a pre trained surrogate, the proposed methodology optimises sensor locations directly within the learning loop. It is based on the Differentiable Sensor Placement Optimisation framework, where the coordinates of a limited number of pressure sensors are treated as continuous trainable variables and jointly optimised with the parameters of a multilayer perceptron (MLP) used for full field reconstruction. A differentiable sampling operator allows gradients to propagate with respect to both network weights and sensor coordinates, enabling true end to end bi level optimisation of the reconstruction model and the measurement layout. The approach is assessed on an open-source database of 150 steady aerodynamic cases based on the NASA Common Research Model. The problem is reduced to a two-dimensional reconstruction of the pressure field on the upper wing surface. First, controlled initialisations are used to compare configurations with 4, 8, and 16 sensors. The normalised root mean square error demonstrates a systematic decrease in both training and test errors as the number of sensors increases, with competitive performance relative to a PODNN-based surrogate reference. Second, 50 independent runs with random initialisations and 4 sensors are conducted to analyse the robustness and spatial distribution of the optimised sensor locations. These are precisely the areas where pressure variations are most informative for global load redistribution and control authority, indicating that the optimisation is not merely numerical but physically meaningful. These results indicate that differentiable sensor placement provides not only improved reconstruction accuracy with very sparse measurements, but also physically interpretable insight into optimal aerodynamic instrumentation strategies.