Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data

By Maizar Raissi, Alireza Yazdani, G. Em Karniadakis. 2018

174 citations recorded by the source corpus.

We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the underlying conservation laws (i.e., for mass, momentum, and energy) to infer hidden quantities of interest such as velocity and pressure fields merely from spatio-temporal visualizations of a passive scaler (e.g., dye or smoke), transported in arbitrarily complex domains (e.g., in human arteries or brain aneurysms). Our approach towards solving the aforementioned data assimilation problem is unique as we design an algorithm that is agnostic to the geometry or the initial and boundary conditions. This makes HFM highly flexible in choosing the spatio-temporal domain of interest for data acquisition as well as subsequent training and predictions. Consequently, the predictions made by HFM are among those cases where a pure machine learning strategy or a mere scientific computing approach simply cannot reproduce. The proposed algorithm achieves accurate predictions of the pressure and velocity fields in both two and three dimensional flows for several benchmark problems motivated by real-world applications. Our results demonstrate that this relatively simple methodology can be used in physical and biomedical problems to extract valuable quantitative information (e.g., lift and drag forces or wall shear stresses in arteries) for which direct measurements may not be possible.

Subfields: Atmospheric Science, Computer Vision and Pattern Recognition, Electrical and Electronic Engineering

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Citations in the corpus

Understanding and mitigating gradient pathologies in physics-informed neural networks (2020, background): “Although such approaches appear seemingly straightforward and have yielded remarkable results across a range of problems in computational science and engineering [19, 20, 21, 22, 23, 24, 25, 26] , the effects of the regularization mechanism in equation 1 remain poorly understood, and in several case”
fPINNs: Fractional Physics-Informed Neural Networks (2018, methodology): “The recent applications of PINNs include (1) inferring the velocity and pressure fields from the concentration field of a passive scalar in solving the Navier--Stokes equations [37] and (2) identifying the distributed parameters of stochastic PDEs [51].”
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, background): “Other studies have targeted the unsupervised learning of divergence-free corrections [57] or incorporated PDE-based loss functions to represent individual flow solutions via ANNs [43, 52].”
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems (2019, background): “, solute concentration [23], and (2) estimation of the unknown constitutive relationship in the nonlinear diffusion equation for unsaturated flows [24].”
Multiscale modeling meets machine learning: What can we learn? (2019, methodology): “More recently, efforts have been made to directly bake theory into machine learning practice [99].”
Learning to Control PDEs with Differentiable Physics (2020, methodology): “, 2019) or used PDE formulations for unsupervised optimization (Raissi et al., 2018).”
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture (2019, methodology): “Methods PINN Architecture Integration points Failure load (N) Benchmark [13] – – 687 VE-PINN∗ [2, 50, 50, 50, 3] 61,440 (960× 64) 670 R-PINN did not converge VE-PINN2† [2, 50, 50, 50, 50, 50, 3] 72,900 (300× 81× 3) 820 ∗VE-PINN = variational energy based PINN (proposed approach) R-PINN = residual ba”
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations (2019, background): “The recent development of PINNs has been well established for forward and inverse problem of solving differential equations [30, 32, 39, 29] and”
Efficient training of physics‐informed neural networks via importance sampling (2021, unknown): “, 2019), (4) uncertainty quantification (e.g., Meng & Karniadakis, 2019; Kissas et al., 2019; Nabian & Meidani, 2019; Raissi et al., 2018; Raissi, Wang, et al., 2019; Xu & Darve, 2019; Y. Yang & Perdikarisa, 2019; Zhu et al., 2019), (5) solving stochastic PDEs (e.”
Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences (2019, methodology): “The focus in the biology, biomedicine, and behavioral sciences is currently shifting from solving forward problems based on sparse data towards solving inverse problems to explain large data sets [Raissi et al., 2018].”
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs (2020, methodology): “This is seen in the robustness and accuracy of the results (see [44,53,54] and references therein).”
Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data (2020, methodology): “[26] were applied to reconstruct a flow field by assimilating scalar concentration data of a flow field [30].”