Author: Jian-Xun Wang

Will host a mini-symposium at SIAM AN 21 (July 19-23), and Xinyang will give a presentation on MBRL for control.

Posted on by Jian-Xun Wang

Together with Prof. Huan Xun@University of Michigan, we will host a two-section mini-symposium (MS48) entiled: Physics-aware machine learning for solving and discovering PDEs, part I (MS48) and part II (MS105)

Part I (MS 48), Tuesday, July 20

  • 4:30-4:55 Deep Neural Network Modeling of Unknown PDEs in Nodal Space abstract Zhen Chen, Ohio State University, U.S.; updated Victor Churchill, Dartmouth College, U.S.; Kailiang Wu and Dongbin Xiu, Ohio State University, U.S. 
  • 5:00-5:25 Deep Learning Methods for Discovering Physics from Data abstract Joseph Bakarji, Jared L. Callaham, and Kathleen Champion, University of Washington, U.S.; J. Nathan Kutz, University of Washington, Seattle, U.S.; Steve Brunton, University of Washington, U.S.
  • 5:30-5:55 Data-Driven Learning of Nonlocal Models:from High-Fidelity Simulations to Constitutive Laws abstract Yue Yu and Huaiqian You, Lehigh University, U.S.; Stewart Silling and Marta D’Elia, Sandia National Laboratories, U.S. 
  • 6:00-6:25 Physics-informed Dyna-Style Model-Based Deep Reinforcement Learning for Dynamic Control abstractupdated Xinyang Liu and Jianxun Wang, University of Notre Dame, U.S.

Part II (MS 105), Friday, July 23

  • 3:30-3:55 Optimal Experimental Design for Variational System Identification of Material Physics Phenomena abstract Wanggang Shen, Zhenlin Wang, Krishna Garikipati, and updated Xun Huan, University of Michigan, U.S. 
  • 4:00-4:25 Learning Stochastic Closures Using Sparsity-Promoting Ensemble Kalman InversionabstractJinlong Wu, Tapio Schneider, and Andrew Stuart, California Institute of Technology, U.S. 
  • 4:30-4:55 PhyCRNet: Physics-Informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEsabstractupdated Pu Ren and Chengping Rao, Northeastern University, U.S.; Jianxun Wang, University of Notre Dame, U.S.; Yang Liu and Hao Sun, Northeastern University, U.S. 
  • 5:00-5:25 Practical Uncertainty Quantification for Learning Partial Differential Equations from Data with Deep EnsemblesabstractSteven Atkinson and Panagiotis Tsilifis, GE Global Research, U.S.

Two new publications in Physics of Fluids (editor’s Pick and featured articles)

Posted on by Jian-Xun Wang
  • 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]

Our group will give 3 talks and a poster at SIAM CSE 2021

Posted on by Jian-Xun Wang

I will organize a mini-symposium entitled “Physics Informed Learning for Modeling and Discovery of Complex Systems” Parts I and II on 03/03/2021 at SIAM CSE. Moreover, our group will also give several talks at CSE21.

MS Talk: Wang et al. Physics-Informed Discretization-Based Learning: a Unified Framework for Solving PDE-Constrained Forward and Inverse Problem (2:15-2:30 CST, 03/03/2021) https://meetings.siam.org/sess/dsp_talk.cfm?p=108358

MS Talk: Han et al. Suppreresolution and Denoising of Flow Imaging using Physics-Constrained Discrete Learning (4:35-4:50 CST, 03/01/2021) https://meetings.siam.org/sess/dsp_talk.cfm?p=108020

MS Talk: Sun et al. System Identification by Sparse Bayesian Learinng (5:35-5:50 CST, 03/04/2021) https://meetings.siam.org/sess/dsp_talk.cfm?p=108437

Poster: Pan et al. Patient-Specific CFD Modeling of Aortic Dissection Augmented with 4D Flow MRI https://meetings.siam.org/sess/dsp_talk.cfm?p=110813

New publication in Computational Mechanics

Posted on by Jian-Xun Wang

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.

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

Posted on by Jian-Xun Wang
  • 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.