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The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally demanding.…

Machine Learning · Computer Science 2025-12-02 Saif Ur Rehman , Wajid Yousuf

Physics-informed neural networks (PINNs) offer a promising framework by embedding partial differential equations (PDEs) into the loss function together with measurement data, making them well-suited for inverse problems. However, standard…

Fluid Dynamics · Physics 2026-05-25 Kakeru Ueda , Hiro Wakimura , Satoshi Ii

Physics-informed neural networks (PINNs) are employed to solve the classical compressible flow problem in a converging-diverging nozzle. This problem represents a typical example described by the Euler equations, thorough understanding of…

Fluid Dynamics · Physics 2023-07-10 Liang Hong , Song Zilong , Zhao Chong , Bian Xin

Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…

Fluid Dynamics · Physics 2025-04-01 Yongzheng Zhu , Weizheng Chen , Jian Deng , Xin Bian

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs…

Machine Learning · Computer Science 2023-11-01 Junwoo Cho , Seungtae Nam , Hyunmo Yang , Seok-Bae Yun , Youngjoon Hong , Eunbyung Park

Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions.…

Fluid Dynamics · Physics 2025-11-19 Ali Eidi , Tyler Buchanan , Letian Jiang , Richard P. Dwight

Accurately resolving steady electrohydrodynamic (EHD) flows presents a formidable computational challenge due to the strong nonlinear coupling between charged-particle density, velocity fields, and electric potential. These interactions…

Computational Physics · Physics 2026-03-24 Chao Lin , Ze Tao , Fujun Liu

Physics-Informed Neural Networks (PINNs) have shown great potential in the context of fluid dynamics simulations, particularly in reconstructing flow fields and identifying key parameters. In this study, we explore the application of PINNs…

Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconstruction of turbulent flow fields from sparse data. However,…

Machine Learning · Computer Science 2026-04-21 Khemraj Shukla , Zongren Zou , Theo Kaeufer , Michael Triantafyllou , George Em Karniadakis

Large-scale river models are being refined over coastal regions to improve the scientific understanding of coastal processes, hazards and responses to climate change. However, coarse mesh resolutions and approximations in physical…

Fluid Dynamics · Physics 2023-03-15 Dongyu Feng , Zeli Tan , QiZhi He

We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By…

High Energy Physics - Theory · Physics 2025-09-17 Koji Hashimoto , Koichi Kyo , Masaki Murata , Gakuto Ogiwara , Norihiro Tanahashi

In this paper, a meshfree method using physics-informed neural networks (PINNs) is developed for solving two-phase flow problems with moving interfaces, where two immiscible fluids bearing different material properties, are separated by a…

Numerical Analysis · Mathematics 2026-04-02 Qijia Zhai , Pengtao Sun , Xiaoping Xie , Xingwen Zhu , Chen-Song Zhang

In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy…

Machine Learning · Computer Science 2024-05-08 Zhihui Li , Francesco Montomoli , Sanjiv Sharma

Though PINNs (physics-informed neural networks) are now deemed as a complement to traditional CFD (computational fluid dynamics) solvers rather than a replacement, their ability to solve the Navier-Stokes equations without given data is…

Fluid Dynamics · Physics 2022-07-26 Pi-Yueh Chuang , Lorena A. Barba

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

Machine Learning · Computer Science 2023-10-02 Sidney Besnard , Frédéric Jurie , Jalal M. Fadili

Presently, there is a steady state approach in Computational fluid dynamics (CFD) to obtain a steady solution directly from the steady state governing equations. Whereas, for obtaining a time-periodic flow solution, the present unsteady…

Computational Physics · Physics 2026-05-19 Lakshya Chaplot , Harshita Agarwal , Atul Sharma

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…

Fluid Dynamics · Physics 2022-10-12 Hao Ma , Yuxuan Zhang , Nils Thuerey , Xiangyu Hu , Oskar J. Haidn

We present a physics-inspired neural network (PINN) model for direct prediction of hydrodynamic forces and torques experienced by individual particles in stationary beds of randomly distributed spheres. In line with our findings, it has…

Fluid Dynamics · Physics 2022-03-09 Arman Seyed-Ahmadi , Anthony Wachs

Despite the remarkable progress of physics-informed neural networks (PINNs) in scientific computing, they continue to face challenges when solving hydrodynamic problems with multiple discontinuities. In this work, we propose…

Fluid Dynamics · Physics 2025-05-28 Chuanxing Wang , Hui Luo , Kai Wang , Guohuai Zhu , Mingxing Luo

Near-wall blood flow and wall shear stress (WSS) regulate major forms of cardiovascular disease, yet they are challenging to quantify with high fidelity. Patient-specific computational and experimental measurement of WSS suffers from…

Fluid Dynamics · Physics 2021-07-28 Amirhossein Arzani , Jian-Xun Wang , Roshan M. D'Souza