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In gradient-based aerodynamic optimisation, the functional gradient required by the optimiser can be obtained as a product of adjoint-based functional sensitivities to volume grid nodes and the volume mesh sensitivities to the design parameters. For turbomachinery applications, it is desirable to use the actual blade design variables as degrees of freedom for the optimisation process, but this can lead to tedious programming tasks. As an alternative, a Machine Learning (ML) model is created to mimic and differentiate the blade geometry and the mesh generation processes. The typical ML forward pass is followed by a  back differentiation  operation enabling the computation of the volume mesh derivatives with respect to design parameters. The model is tested by comparing the ML-predicted and reference grid, and the modelled sensitivities are verified through algorithmic differentiation. The modelled mesh sensitivities are successfully employed for adjoint-based reverse engineering and design optimisation problems on a turbine blade.

A Conceptual Alternative Machine Learning-Based Method for Mesh Sensitivities Calculation in a Turbomachinery Blades Optimisation Framework