| 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 |
Author: Jian-Xun Wang
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.
Han Gao receives outstanding teaching awards, Congrats!
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,
Welcome to a new PhD student in our group!
Xinyang is a recent graduate from XJTU (2019) and joined our group this spring. He will work on data assimilation for computational hemodynamics, welcome!
Our work on physics-constrained DL is covered by media
Invited seminar in ME department at the University of Michigan, Ann Arbor.
Dr. Wang will give a seminar talk at University of Michigan, Ann Arbor. Please see the announcement here https://me.engin.umich.edu/sites/default/files/2019-10/Wang%20announcement.pdf
Several presentations at APS DFD 2019, Seattle.
J Wang’s group will give three presentations at 72nd APS-DFD in Seattle,
- J.-X. Wang will present “Surrogate Modeling for Fluid Flows Using Physics-Constrained, Label-Free Deep Learning “,
- Han Gao will present “A Multi-fidelity Ensemble Kalman Method for Inverse Problems in Cardiovascular Flows“,
- Luning Sun will present “Super-resolution and Denoising of Flow MRI Data using Physics-Constrained Deep Learning “
See you in Seattle!
New publication in Computer Methods in Applied Mechanics and Engineering
L. Sun*, H. Gao*, S. Pan, J.-X. Wang. Surrogate Modeling for Fluid Flows Based on Physics- Constrained Deep Learning Without Simulation Data. Computer Methods in Applied Mechanics and Engineering, 2019 (Forthcoming), see preprint
Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation into the finite-dimensional algebraic system solved by computers. Due to complicated nature of the physics and geometry, such process can be computational prohibitive for most real-time applications and many-query analyses. Therefore, developing a cost-effective surrogate model is of great practical significance. Deep learning (DL) has shown new promises for surrogate modeling due to its capability of handling strong nonlinearity and high dimensionality. However, the off-the-shelf DL architectures fail to operate when the data becomes sparse. Unfortunately, data is often insufficient in most parametric fluid dynamics problems since each data point in the parameter space requires an expensive numerical simulation based on the first principle, e.g., Naiver–Stokes equations. In this paper, we provide a physics-constrained DL approach for surrogate modeling of fluid flows without relying on any simulation data. Specifically, a structured deep neural network (DNN) architecture is devised to enforce the initial and boundary conditions, and the governing partial differential equations are incorporated into the loss of the DNN to drive the training. Numerical experiments are conducted on a number of internal flows relevant to hemodynamics applications, and the forward propagation of uncertainties in fluid properties and domain geometry is studied as well. The results show excellent agreement on the flow field and forward-propagated uncertainties between the DL surrogate approximations and the first-principle numerical simulations.
Luning and Han are second-year PhD students in J-X. Wang’s group. Congrats!