Physics-informed neural networks (PINNs) for fluid mechanics: a review
By Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, G. Em Karniadakis. Acta Mechanica Sinica, 2021
2,043 citations recorded by the source corpus.
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 implement 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.
Subfields: Computational Mechanics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8efcb1e84f617841520ae9f0c26cb1cd214b0af5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- G. Em Karniadakis
- Zhiping Mao
- Lu Lu
- Maizar Raissi
- Shengze Cai
- Xuhui Meng
- Khemraj Shukla
- Zhongqiang Zhang
In Statistical and Nonlinear Physics
- G. Em Karniadakis
- Lu Lu
- Zhiping Mao
- Xuhui Meng
- Maizar Raissi
- Gianluigi Rozza
- Shengze Cai
- Fabio Giampaolo
Citations in the corpus
- Physics-Informed Neural Operator for Learning Partial Differential Equations (2021, neutral): “For example, in challenging problems such as turbulence, PINNs are only able to solve the PDE on a relatively small domain [44], or otherwise, require extra observational data which is not always available in practice [31, 45].”
- Physics‐Informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions (2021, methodology): “…DNNs and have been successfully applied to various problems in engineering and biology with applications including but not limited to heat transfer (Cai et al., 2021), solution of Navier-Stokes equations in fluid mechanics (Jin et al., 2021), high speed fluid flow (Mao et al., 2020) and solid…”
- Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “, cyber-physical systems [223], chemistry [205], medical imaging [175], fluid mechanics [46], climate and weather[146]).”
- A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data (2021, background): “Physics-informed neural networks (PINNs) were introduced first in 2017 [7, 8] for forward, inverse and hybrid problems, and since then there have also been rapid developments in this area [9, 10, 11, 12, 13, 14, 15, 16, 17], although the achievements so far in scientific and engineering applications”
- Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, methodology): “Moreover the governing equations in dimensionless form, including the Stokes equations, electric potential, and ion transport equations, are presented in DeepM&Mnets (Cai et al, 2021b).”
- Analyses of internal structures and defects in materials using physics-informed neural networks (2022, neutral): “L u (, ) = 1 ─ N u ∑ i=1 N u ∣ ̃ ru (i) ( ) ∣ 2 (15)”