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Physics-informed neural networks (PINNs) have attracted considerable attention for their ability to integrate partial differential equation priors into deep learning frameworks; however, they often exhibit limited predictive accuracy when…

Machine Learning · Computer Science 2026-05-28 Ze Tao , Hanxuan Wang , Fujun Liu

Physics-informed neural networks (PINNs) demonstrate promising potential in parameterized engineering turbulence optimization problems but face challenges, such as high data requirements and low computational accuracy when applied to…

Fluid Dynamics · Physics 2025-03-25 Liang Jiang , Yuzhou Cheng , Kun Luo , Jianren Fan

The recent surge of interest in physics-informed neural network (PINN) methods has led to a wave of studies that attest to their potential for solving partial differential equations (PDEs) and predicting the dynamics of physical systems.…

Computational Engineering, Finance, and Science · Computer Science 2023-06-02 Pi-Yueh Chuang , Lorena A. Barba

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) integrate physical principles into machine learning, finding wide applications in various science and engineering fields. However, solving nonlinear hyperbolic partial differential equations (PDEs)…

Fluid Dynamics · Physics 2024-10-01 Jingjing Zhang , Ulisses Braga-Neto , Eduardo Gildin

Deep neural networks are being increasingly used for short-term traffic flow prediction, which can be generally categorized as convolutional (CNNs) or graph neural networks (GNNs). CNNs are preferable for region-wise traffic prediction by…

Physics and Society · Physics 2021-10-12 Wei Zeng , Chengqiao Lin , Kang Liu , Juncong Lin , Anthony K. H. Tung

Electrical submersible pumps (ESPs) are prevalently utilized as artificial lift systems in the oil and gas industry. These pumps frequently encounter multiphase flows comprising a complex mixture of hydrocarbons, water, and sediments. Such…

Machine Learning · Computer Science 2024-10-03 Felipe de Castro Teixeira Carvalho , Kamaljyoti Nath , Alberto Luiz Serpa , George Em Karniadakis

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

Flood models inform strategic disaster management by simulating the spatiotemporal hydrodynamics of flooding. While physics-based numerical flood models are accurate, their substantial computational cost limits their use in operational…

The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…

Fluid Dynamics · Physics 2026-02-24 Jiahao Song , Wenbo Cao , Weiwei Zhang

Two-phase flow phenomena underpin critical technologies such as hydrogen fuel cells, spray cooling, and combustion, where droplet dynamics govern performance and efficiency. Conventional optical diagnostics, including shadowgraphy and…

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

Physics-informed neural networks (PINNs) have been applied to simulate multiphase flows, yet they are limited in modeling phase changes and sharp interfaces due to optimization conflicts in the strongly coupled Allen-Cahn, Cahn-Hilliard,…

Computational Physics · Physics 2026-01-22 Guoqiang Lei , Zhihua Wang , Lijing Zhou , D. Exposito , Xuerui Mao

When a fluid flows over a solid surface, it creates a thin boundary layer where the flow velocity is influenced by the surface through viscosity, and can transition from laminar to turbulent at sufficiently high speeds. Understanding and…

Fluid Dynamics · Physics 2024-10-24 Matthew Bonas , David H. Richter , Stefano Castruccio

Accurately and stably solving the incompressible Navier--Stokes equations with physics-informed neural networks (PINNs) remains challenging, particularly for sparse or noisy observations and for flow regimes in which the local balance among…

Fluid Dynamics · Physics 2026-03-31 Ke Xu , Ze Tao , Fujun Liu

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

Computational Engineering, Finance, and Science · Computer Science 2022-01-26 Han Gao , Matthew J. Zahr , Jian-Xun Wang

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

Fluid Dynamics · Physics 2024-11-14 Chuyu Zhou , Tianyu Li , Chenxi Lan , Rongyu Du , Guoguo Xin , Pengyu Nan , Hangzhou Yang , Guoqing Wang , Xun Liu , Wei Li

Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…

Machine Learning · Computer Science 2026-03-18 Chenglin Li , Hang Xu , Jianting Chen , Yanfei Zhang

Physics-Informed Neural Networks have emerged as a promising methodology for solving PDEs, gaining significant attention in computer science and various physics-related fields. Despite being demonstrated the ability to incorporate the…

Machine Learning · Computer Science 2025-05-01 Yao-Hsuan Tsai , Hsiao-Tung Juan , Pao-Hsiung Chiu , Chao-An Lin
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