Physics-informed neural networks (PINNs) for fluid mechanics: A review

TL;DR

This review discusses physics-informed neural networks (PINNs) as a promising approach to integrate data and physics for fluid mechanics problems, addressing challenges like noisy data, complex geometries, and high-dimensionality.

Contribution

The paper provides a comprehensive review of PINNs in fluid mechanics, highlighting their ability to solve inverse problems and integrate data with Navier-Stokes equations.

Findings

PINNs effectively handle inverse flow problems.

PINNs demonstrate success in 3D wake, supersonic, and biomedical flows.

PINNs offer a seamless integration of data and physics.

Abstract

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.