Discontinuity Computing Using Physics-Informed Neural Networks

Download This Paper Open PDF in Browser Add Paper to My Library Share: Permalink Using these links will ensure access to this page indefinitely Copy URL Discontinuity Computing Using Physics-Informed Neural Networks 20 Pages Posted: 20 Sep 2022 See all articles by Li LiuLi LiuInstitute of Applied Physics and Computational MathematicsShengping LiuInstitute of Applied Physics and Computational Mathematics - Laboratory of Computational PhysicsHui XieInstitute of Applied Physics and Computational MathematicsFansheng XiongInstitute of Applied Physics and Computational MathematicsTengchao YuInstitute of Applied Physics and Computational MathematicsMengjuan XiaoInstitute of Applied Physics and Computational MathematicsLufeng LiuInstitute of Applied Physics and Computational MathematicsHeng YongInstitute of Applied Physics and Computational Mathematics - Laboratory of Computational Physics Abstract Simulating discontinuities is a long standing problem particularly for shock waves with strong nonlinear features. Despite being a promising method, the recently developed physics-informed neural networks (PINNs) are still not fully effective for calculating discontinuities compared with those of traditional shock-capturing methods. In this study, we first reveal that the training of PINNs may fall into paradoxical phenomenon when simulating problems with strong discontinuities. Intend to break the paradox and improve the shock-capturing ability of the PINNs, we propose a strategy to weaken the expression of the neural network (NN) near discontinuities by adding a physics-dependent weight into the governing equations locally at each residual point. Correspondingly, the NN will focus on training the smooth parts of the solutions. Then, automatically affected by the compressible property, a sharp discontinuity appears with transition points inside the shock waves compressed into well-trained smooth regions as passive particles. To demonstrate the effect of the new method, we study one-dimensional Burgers equation and one- and two-dimensional Euler equations. Compared with a traditional high-order weighted essential non-oscillatory (WENO) method in the numerical examples, the proposed weighted-equations PINNs (PINNs-WE) method can substantially improve discontinuity computing. Keywords: Physics-informed neural networks, Shock capturing, Compressible flow, Euler equations, Discontinuity calculation Suggested Citation: Suggested Citation Liu, Li and Liu, Shengping and Xie, Hui and Xiong, Fansheng and Yu, Tengchao and Xiao, Mengjuan and Liu, Lufeng and Yong, Heng, Discontinuity Computing Using Physics-Informed Neural Networks. Available at SSRN: https://ssrn.com/abstract=4224074 Li Liu (Contact Author) Institute of Applied Physics and Computational Mathematics ( email ) Fenghao East Road 2BeijingChina Shengping Liu Institute of Applied Physics and Computational Mathematics - Laboratory of Computational Physics ( email ) Beijing, 100094China Hui Xie Institute of Applied Physics and Computational Mathematics ( email ) Fenghao East Road 2BeijingChina Fansheng Xiong Institute of Applied Physics and Computational Mathematics ( email ) Fenghao East Road 2BeijingChina Tengchao Yu Institute of Applied Physics and Computational Mathematics ( email ) Fenghao East Road 2BeijingChina Mengjuan Xiao Institute of Applied Physics and Computational Mathematics ( email ) Fenghao East Road 2BeijingChina Lufeng Liu Institute of Applied Physics and Computational Mathematics ( email ) Fenghao East Road 2BeijingChina Heng Yong Institute of Applied Physics and Computational Mathematics - Laboratory of Computational Physics ( email ) Beijing, 100094China Download This Paper Open PDF in Browser Do you have a job opening that you would like to promote on SSRN? Place Job Opening Paper statistics Downloads 0 Abstract Views 2 PlumX Metrics Feedback Feedback to SSRN Feedback (required) Email (required) Submit If you need immediate assistance, call 877-SSRNHelp (877 777 6435) in the United States, or +1 212 448 2500 outside of the United States, 8:30AM to 6:00PM U.S. Eastern, Monday - Friday. Submit a Paper Section 508 Text Only Pages SSRN Quick Links SSRN Solutions Research Paper Series Conference Papers Partners in Publishing Jobs & Announcements Newsletter Sign Up SSRN Rankings Top Papers Top Authors Top Organizations About SSRN SSRN Objectives Network Directors Presidential Letter Announcements Contact us FAQs Copyright Terms and Conditions Privacy Policy We use cookies to help provide and enhance our service and tailor content. To learn more, visit Cookie Settings. This page was processed by aws-apollo-5dc in 0.275 seconds