| The implementation of differentiated Deep Neural Networks (DNNs), within a gradient-based optimization method in fluid mechanics, for predicting the objective function values and its gradient, is demonstrated and assessed. In the proposed method, DNNs, after being trained on a set of patterns for which the objective function values are available, are used to replace both the code simulating the fluid flow and its adjoint solver computing gradients in problems governed by partial differential equations. The derivatives of the responses of the trained DNNs with respect to its inputs (which are the design variables of the optimization problem) are computed using automatic differentiation in reverse accumulation mode. Prior to successfully and efficiently supporting the optimization loop, gradients are verified against finite differences as well as the adjoint method. The proposed, DNN-driven shape optimization method is used to design an isolated airfoil (inviscid flow) and an S-bend duct (laminar flow); its efficiency is compared with an adjoint-based optimization. |
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