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We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and…

Computational Physics · Physics 2021-03-17 Eric J. Hall , Søren Taverniers , Markos A. Katsoulakis , Daniel M. Tartakovsky

While many recent Physics-Informed Neural Networks (PINNs) variants have had considerable success in solving Partial Differential Equations, the empirical benefits of feature mapping drawn from the broader Neural Representations research…

Machine Learning · Computer Science 2024-04-30 Chengxi Zeng , Tilo Burghardt , Alberto M Gambaruto

Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating…

Quantum Physics · Physics 2025-12-17 Changchun Feng , Laifa Tao , Lin Chen

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

Machine Learning · Computer Science 2024-01-17 Abdul Hannan Mustajab , Hao Lyu , Zarghaam Rizvi , Frank Wuttke

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

Computational Physics · Physics 2024-06-10 Michel Nohra , Steven Dufour

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Machine Learning · Computer Science 2024-09-18 Shivprasad Kathane , Shyamprasad Karagadde

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…

Ultrasound and radar signals are highly beneficial for medical imaging as they are non-invasive and non-ionizing. Traditional imaging techniques have limitations in terms of contrast and physical interpretation. Quantitative medical imaging…

Computer Vision and Pattern Recognition · Computer Science 2024-02-19 Tom Sharon , Yonina C. Eldar

The aim of this paper is to introduce a Mapping-based Hard-constrained Physics-Informed Neural Network (MH-PINN) for efficiently and accurately solving unbounded wave problems. First, we propose a coordinate mapping technique that…

Numerical Analysis · Mathematics 2026-04-23 Tao Zhang , Hanshu Chen , Ilia Marchevsky , Zhuojia Fu

A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schr\"odinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and…

Optics · Physics 2021-09-03 Xiaotian Jiang , Danshi Wang , Qirui Fan , Min Zhang , Chao Lu , Alan Pak Tao Lau

The neutron diffusion equation plays a pivotal role in the analysis of nuclear reactors. Nevertheless, employing the Physics-Informed Neural Network (PINN) method for its solution entails certain limitations. Traditional PINN approaches…

Machine Learning · Computer Science 2024-07-17 Heng Zhang , Yun-Ling He , Dong Liu , Qin Hang , He-Min Yao , Di Xiang

This paper proposes a rank inspired neural network (RINN) to tackle the initialization sensitivity issue of physics informed extreme learning machines (PIELM) when numerically solving partial differential equations (PDEs). Unlike PIELM…

Numerical Analysis · Mathematics 2025-06-24 Wentao Peng , Yunqing Huang , Nianyu Yi

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and…

Accurate multiple-input multiple-output (MIMO) channel estimation is critical for next-generation wireless systems, enabling enhanced communication and sensing performance. Traditional model-based channel estimation methods suffer, however,…

Signal Processing · Electrical Eng. & Systems 2026-02-02 Seyed Alireza Javid , Nuria González-Prelcic

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Computational Engineering, Finance, and Science · Computer Science 2022-01-07 Mayank Raj , Pramod Kumbhar , Ratna Kumar Annabattula

We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the…

Machine Learning · Computer Science 2020-05-09 Khemraj Shukla , Patricio Clark Di Leoni , James Blackshire , Daniel Sparkman , George Em Karniadakis

Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…

Computational Physics · Physics 2026-02-13 Nilufer K. Bulut

Magnetic resonance imaging (MRI) is an important non-invasive imaging method in clinical diagnosis. Beyond the common image structures, parametric imaging can provide the intrinsic tissue property thus could be used in quantitative…

Image and Video Processing · Electrical Eng. & Systems 2023-09-22 Qingrui Cai , Liuhong Zhu , Jianjun Zhou , Chen Qian , Di Guo , Xiaobo Qu

Wireless imaging has become a vital function in future integrated sensing and communication (ISAC) systems. However, traditional model-based and data-driven deep learning imaging methods face challenges related to multipath extraction,…

Information Theory · Computer Science 2026-02-13 Yixuan Huang , Jie Yang , Chao-Kai Wen , Shi Jin

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…