Physics-informed neural networks (PINNs) for fluid mechanics: A review
This is a review paper, so it is incremental, summarizing existing methods rather than introducing new ones.
The paper reviews physics-informed neural networks (PINNs) for fluid mechanics, addressing challenges like incorporating noisy data, mesh generation, and high-dimensional inverse problems, and demonstrates their effectiveness in applications such as three-dimensional wake flows, supersonic flows, and biomedical flows.
Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implementing them using physics-informed neural networks (PINNs). We demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows.