A reduced order finite element-informed surrogate model for approximating global high-fidelity simulation

Surrogate model is an efficient tool to replace the high-fidelity (HF) simulations governed by partial differential equations (PDEs) to obtain response under different parameters (e.g., external force, density). However, due to the huge computational burden, large sampling size, and high dimension, the traditional surrogate model may be infeasible to predict global high-dimensional simulation under different parameters accurately. To tackle these issues, this study proposes a reduced order finite element (ROFE)-informed surrogate model for fast approximating the global HF simulation based on reduced order modeling (ROM), which mainly consists of two parts: (1) A reduced order surrogate model framework is designed based on the proper orthonormal decomposition and feedforward neural network to approximate the HF simulations with different parameters. (2) A new loss function and a hybrid training scheme is proposed based on an extra ROFE information to enhance network training, thereby avoiding non-convergence when using limited data. The proposed method is tested on three problems, including two numerical cases and one engineering case, and compared with the traditional ROM method, data-driven ROM method, and physics-informed neural network. The results indicate that the proposed surrogate model provides a cost-effective way to approximate the global HF simulation. The time spent and data requirement are less than that of other methods under the same accuracy. Finally, the proposed method has been successfully applied in a real engineering application to estimate the drag and lift coefficients of airfoil, which is closer to experimental results than XFOIL and with a high speed (about 10⁻⁶ s).