In fluids engineering design and Multidisciplinary Design Optimization (MDO), it is a major issue to reduce the number of iteration of the numerical simulation such as Computational Fluid Dynamics (CFD) and to reduce the computational cost of each simulation on it. An AI-enhanced surrogate model system, which is composed of a main surrogate model for reducing the number of iteration and a sub surrogate model for reducing the simulation cost, is presented. The efficiency of the system can be multiplicatively enhanced by combination of the main and sub surrogate models. The main surrogate model is designed as a Bayesian model to efficiently guide the iterative process of the numerical simulations in computational mechanics. There are various types of possible models such as Gaussian process (GP) regression models with hierarchy to treat multi-fidelity data [1], Bayesian neural networks (BNNs) and multi-fidelity BNNs [2]. To maintain closes-form expressions in the prediction process of the model when multi-fidelity data and further additional offline data with counting also governing equations in physics and expert knowledge among it, a generalized GP regression model is developed as the main surrogate model. Results using various test functions show that the surrogate model achieves higher accuracy than ordinary GP models and multi-fidelity GP models under the same cost. The sub surrogate model is to assist the computational cost to generate a sample point by the numerical simulation of the main surrogate model. Since the accuracy of high-dimensional predicted output is demanded in the whole input space, deterministic function approximation models such as neural network models can be suitable in contrast to the main surrogate model. Examples of the sub surrogate model is presented by demonstrating flow analysis around two-dimensional airfoil configurations using graph neural networks as one of the promising models to integrate numerical schemes and/or physics such as physics-informed neural networks.