Gaining and understanding the flow dynamics have much importance in a wide range of disciplines, e.g. astrophysics, geophysics, biology, mechanical engineering and biomedical engineering. As a reliable way in practice, especially for turbulent flows, regional flow information such as velocity and its statistics, can be measured experimentally. Due to the poor fidelity or other technical limitations, some information may not be resolved in a region of interest. On the other hand, detailed flow features are described by the governing equations, e.g. the Navier-Stokes equations for viscous fluid, and can be resolved numerically, which is heavily dependent on the capability of either computing resources or modelling. Alternatively, we address this problem by employing the physics-informed deep learning, and treat the governing equations as a parameterised constraint to recover the missing flow dynamics. We demonstrate that with limited data, no matter from experiment or others, the flow dynamics in the region where the required data is missing or not measured, can be reconstructed with the parameterised governing equations. Meanwhile, a richer dataset, with spatial distribution of the control parameter (e.g. eddy viscosity of turbulence modellings), can be obtained. The method provided in this paper may shed light on data-driven scale-adaptive turbulent structure recovering and understanding of complex fluid physics, and can be extended to other parameterised governing systems beyond fluid mechanics.
PINNs4Drops: Video-conditioned physics-informed neural networks for two-phase flow reconstruction
Department One（第一系）；Department Two（第二系）；Institute of Fluid Mechanics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院流体力学研究所）；Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
Physics-informed neural network for inverse modeling of granular flows
College of New Energy Science and Engineering, China University of Petroleum-Beijing（中国石油大学（北京）新能源科学与工程学院）；State Key Laboratory of Heavy Oil Processing, China University of Petroleum-Beijing（中国石油大学（北京）重油加工国家重点实验室）；State Key Laboratory of Deep Geothermal Resources, China University of Petroleum-Beijing（中国石油大学（北京）深层地热资源利用国家重点实验室）
Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS
Pennsylvania State University（宾夕法尼亚州立大学）；CSIR-National Aerospace Laboratories（印度国家航空航天实验室）；Case Western Reserve University（凯斯西储大学）；National Research Council Canada（加拿大国家研究委员会）
Hard Constraint Projection in a Physics Informed Neural Network
University of Leeds School of Computing, School of Civil Engineering（利兹大学计算机学院、土木工程学院）；University College London Department of Computer Science（伦敦大学学院计算机科学系）
A Physics-Informed Spatiotemporal Deep Learning Framework for Turbulent Systems
Department of Applied and Computational Mathematics and Statistics, University of University of Notre Dame（应用与计算数学与统计学系，诺特大学）；Department of Environmental and Civil Engineering, University of Notre Dame（环境与土木工程系，诺特大学）
Bayesian Reasoning for Physics Informed Neural Networks
Institute for Theoretical Physics, University of Wroc aw（沃拉夫大学理论物理研究所）；Institute of Low Temperature and Structure Research（低温与结构研究所）；Polish Academy of Sciences（波兰科学院）
