New Publication in JCP: Physics-Informed Geometry-Adaptive Convolutional Neural Networks

  • H. Gao*, L. Sun, J.-X. Wang, PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parametric PDEs on Irregular Domain. Journal of Computational Physics, 428, 110079, 2021 [ArxivDOI, bib]

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all different classes of deep neural networks, the convolutional neural network (CNN) has attracted increasing attention in the scientific machine learning community, since the parameter-sharing feature in CNN enables efficient learning for problems with large-scale spatiotemporal fields. However, one of the biggest challenges is that CNN only can handle regular geometries with image-like format (i.e., rectangular domains with uniform grids). In this paper, we propose a novel physics-constrained CNN learning architecture, aiming to learn solutions of parametric PDEs on irregular domains without any labeled data. In order to leverage powerful classic CNN backbones, elliptic coordinate mapping is introduced to enable coordinate transforms between the irregular physical domain and regular reference domain. The proposed method has been assessed by solving a number of steady-state PDEs on irregular domains, including heat equations, Navier-Stokes equations, and Poisson equations with parameterized boundary conditions, varying geometries, and spatially-varying source fields. Moreover, the proposed method has also been compared against the state-of-the-art PINN with fully-connected neural network (FC-NN) formulation. The numerical results demonstrate the effectiveness of the proposed approach and exhibit notable superiority over the FC-NN based PINN in terms of efficiency and accuracy.

Our group will give 4 talks at 73rd Annual Meeting of APS Division of Fluid Dynamics

Please check out our presentations at APS DFD:

R01.00011: Super-resolution and Denoising of Fluid Flows Using Physics-informed Convolutional Neural Networks

Jian-Xun Wang, Han Gao, Luning Sun

R01.00038: A unifying framework of solving forward and inverse problems in fluid mechanics via deep learning
Han Gao, Jian-Xun Wang

R10.00002 Physics-constrained multi-fidelity convolutional neural networks for surrogate fluid modeling 
Luning Sun, Han Gao, Jian-Xun Wang

W07.00012 Computational simulation of aortic dissection with a comparison with 4D flow MRI 
Pan Du, Nicholas Burris, Julio Sotelo, Jian-Xun Wang

http://meetings.aps.org/Meeting/DFD20/Content/3927 

Department Seminar at IUPUI (Virtual)

Speaker: Jian-Xun Wang, Date / Time: Nov. 12, 2020, 11:00 – 12:00 pm, Location: (Virtual)

Abstract

Recent advances in data science techniques, combined with the ever-increasing availability of high-fidelity simulation/measurement data open up new opportunities for developing data-enabled computational modeling of fluid systems. However, compared to most computer science applications, the cost of data acquisition for modeling complex physical/physiological systems is usually expensive or even prohibitive, which poses challenges for directly leveraging the success of existing deep learning models. On the other hand, there is often richness of prior knowledge, including physical laws and phenomenological principles, which can be leveraged to enable efficient learning in the “small data” regime. This talk will focus on physics-informed deep learning (PIDL), which has recently attracted increasing attention in the scientific machine learning community. The objective is to enable effective learning in a data-scarce setting by incorporating physics knowledge (e.g., conservation laws) to inform the learning architecture construction and/or constrain the training process. Our recent developments in PIDL for, e.g., surrogate modeling, super-resolution, and uncertainty quantification, will be presented. The effectiveness of the proposed methods will be demonstrated on a number of fluid problems that are relevant to hemodynamic applications. 

New publication: Physics-Constrained Bayesian Neural Network for Fluid Flow Reconstruction with Sparse and Noisy Data in TAML

L. Sun*, J.-X. Wang, Physics-Constrained Bayesian Neural Network for Fluid Flow Reconstruction with Sparse and Noisy Data, Theoretical and Applied Mechanics Letters, (Accepted), 2020 [Arxiv, DOI, bib]

In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an innovative physics-constrained Bayesian deep learning approach to reconstruct flow fields from sparse, noisy velocity data, where equation-based constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated. Specifically, a Bayesian deep neural network is trained on sparse measurement data to capture the flow field. In the meantime, the violation of physical laws will be penalized on a large number of spatiotemporal points where measurements are not available. A non-parametric variational inference approach is applied to enable efficient physics-constrained Bayesian learning. Several test cases on idealized vascular flows with synthetic measurement data are studied to demonstrate the merit of the proposed method.

 

Department Seminar Talk at CU Boulder, Mar 4th. 2020,

https://www.colorado.edu/center/aerospacemechanics/events/spring-2020-fluids-structure-materials-fsm-seminars

Speaker: Jian-Xun Wang, Date / Time: Wednesday, March 4, 2020, 4:30 – 5:30 pm, Location: AERO 114

Abstract:

Recent advances in data science techniques, combined with the ever-increasing availability of high-fidelity simulation/measurement data open up new opportunities for developing data-enabled computational modeling of fluid systems. However, compared to most applications in the computer science community, the cost of data acquisition for modeling complex physical/physiological systems is usually expensive or even prohibitive, which poses challenges for directly leveraging the success of existing deep learning models. On the other hand, there is usually richness of prior knowledge including physical laws and phenomenological theories, which can be leveraged to enable efficient learning in the “small data” regime. This talk will focus on the data-driven/data-augmented modeling for fluid flows based using physics-constrained machine learning and Bayesian data assimilation techniques, where both the sparse data and physical principles are leveraged. Specifically, several separate but related topics will be covered, including machine learning assisted RANS turbulence modeling, physics-constrained deep learning for fluid surrogate modeling and super-resolution, and multi-fidelity Bayesian data assimilation for field inversion in fluid simulations.

Several presentations at APS DFD 2019, Seattle.

J Wang’s group will give three presentations at 72nd APS-DFD in Seattle,

See you in Seattle!