Finite-Volume Physics-Informed U-Net for Flow Field Reconstruction With Sparse Data

Abstract Fluid dynamics is governed by partial differential equations (PDEs) which are solved numerically. The limitations of traditional methods in data assimilation hinder their effective engagement with experiments. Physics-informed neural network (PINN) has emerged as a hybrid data-physics-driven model for convective problems. However, the approach suffers from low accuracy and poor efficiency due to the way of incorporating PDEs. In this work, a novel convolutional neural network framework integrating the finite volume method (FVM) is developed to address the challenge. The interface variables of the grid are predicted by the neural network for the first time, rather than a complex procedure in FVM. The physical law is then learned by minimizing the residual of the discretized conservative form of PDEs. A comparison between this model and the existing PINN models regarding prediction accuracy demonstrates the superiority of embedding PDEs through FVM. The effects of sampling strategies and quantities are studied. The result confirms the model's capability to utilize sparse measurement data within the computational domain. Furthermore, the model performs well even in scenarios where partial initial and boundary conditions are absent.