  Adjoint method is widely used in aerodynamic design because only once
solution of flow field is required for adjoint method to obtain the gradients
of all design variables. However, the calculation cost of adjoint vector is
approximately equal to that of flow computation. In order to accelerate the
solution of adjoint vector and improve the adjoint-based optimization
efficiency, machine learning for adjoint vector modeling is presented. Deep
neural network (DNN) is employed to construct the mapping between the adjoint
vector and the local flow variables. DNN can efficiently predict adjoint vector
and its generalization is examined by a transonic drag reduction about NACA0012
airfoil. The results indicate that with negligible calculation cost of the
adjoint vector, the proposed DNN-based adjoint method can achieve the same
optimization results as the traditional adjoint method.
