Lastest News

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

Posted on by Jian-Xun Wang

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,

Posted on by Jian-Xun Wang

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.

Posted on by Jian-Xun Wang

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

See you in Seattle!

 

New publication in Computer Methods in Applied Mechanics and Engineering

Posted on by Jian-Xun Wang

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!

Presented PCML paper in USC Workshop on Research Challenges at the interface of Machine Learning and Uncertainty Quantification

Posted on by Jian-Xun Wang

Presented a paper entitled of Surrogate Modeling for Fluid Flows Based on Physics-Constrained, Label-Free Deep Learning at USC Workshop on Research Challenges at the interface of Machine Learning and Uncertainty Quantification. Please check out http://hyperion.usc.edu/MLUQ/agenda.html