$\lambda$-DNNs and Their Implementation in Aerodynamic and Conjugate Heat Transfer Optimization

Abstract

A fully-connected Deep Neural Network (DNN) architecture, to be referred to as $\lambda$-DNN, used to predict 2D/3D scalar fields is presented. In aerodynamics, the $\lambda$-DNN is firstly trained on fields computed using a Computational Fluid Dynamics (CFD) software. Then, it can be incorporated into engineering processes in various ways. One possibility is to use them in optimization problems solved by stochastic population-based methods, in which the $\lambda$-DNN may act as the surrogate evaluation model, replacing calls to the CFD tool. Another possibility is in multi-disciplinary problems, to replicate the numerical solver for any of the disciplines. This small list of possible usages is not exhaustive and, of course, different usages can be combined. The input to each DNN contains information to identify the geometrical shape and case-related data, nodal coordinates and, in multi-disciplinary problems, interfacing data connecting solvers for different disciplines on adjacent domains. In this paper, the $\lambda$-DNN is firstly used in the aerodynamic shape optimization of a wing using evolutionary algorithms, in which it replicates the CFD solver. Then, it is used in a conjugate heat transfer problem dealing with a solid domain in contact with a flow within a duct. In this problem, the $\lambda$-DNN acts as a surrogate to the solver of the heat conduction equation on the solid domain, by interfacing with a CFD solver of the fluid domain.