Category: Publication

Congrats to Pan Du on his first publication in PLoS One

• H. Wu, P. Du*, R. Kokate, J.-X. Wang, A semi-analytical solution and AI-based reconstruction algorithms for magnetic particle tracking, PLoS ONE, 16(7): e0254051, 2021. [Arxiv, DOI, bib]

• 1. H. Gao*, L. Sun, J.-X. Wang, Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels, Physics of Fluids, 33(7), 073603, 2021 (Editors’ Pick) [Arxiv, DOI, bib]

• 2. A. Arzani, J.-X. Wang, R. D’Souza, Uncovering near-wall blood flow from sparse data with physics-informed neural networks, Physics of Fluids, 33, 071905, 2021 (Featured Article) [Arxiv, DOI, bib]

H. Gao*, J.-X. Wang, A Bi-fidelity Ensemble Kalman Method for PDE-Constrained Inverse Problems, Computational Mechanics

https://link.springer.com/article/10.1007/s00466-021-01979-6?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst&utm_source=ArticleAuthorOnlineFirst&utm_medium=email&utm_content=AA_en_06082018&ArticleAuthorOnlineFirst_20210226

Mathematical modeling and simulation of complex physical systems based on partial differential equations (PDEs) have been widely used in engineering and industrial applications. To enable reliable predictions, it is crucial yet challenging to calibrate the model by inferring unknown parameters/fields (e.g., boundary conditions, mechanical properties, and operating parameters) from sparse and noisy measurements, which is known as a PDE-constrained inverse problem. In this work, we develop a novel bi-fidelity (BF) ensemble Kalman inversion method to tackle this challenge, leveraging the accuracy of high-fidelity models and the efficiency of low-fidelity models. The core concept is to build a BF model with a limited number of high-fidelity samples for efficient forward propagations in the iterative ensemble Kalman inversion. Compared to existing inversion techniques, salient features of the proposed methods can be summarized as follow: (1) achieving the accuracy of high-fidelity models but at the cost of low-fidelity models, (2) being robust and derivative-free, and (3) being code non-intrusive, enabling ease of deployment for different applications. The proposed method has been assessed by three inverse problems that are relevant to fluid dynamics, including both parameter estimation and field inversion. The numerical results demonstrate the excellent performance of the proposed BF ensemble Kalman inversion approach, which drastically outperforms the standard Kalman inversion in terms of efficiency and accuracy.

• 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 [Arxiv, DOI, 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.

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.