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Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study…

Materials Science · Physics 2025-10-14 Mohid Farooqi , Ingmar Bösing , Conrard G. Tetsassi Feugmo

Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…

Numerical Analysis · Mathematics 2021-08-18 Yinlin Ye , Yajing Li , Hongtao Fan , Xinyi Liu , Hongbing Zhang

We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…

Optimization and Control · Mathematics 2019-02-19 Daniela di Serafino , Gerardo Toraldo , Marco Viola , Jesse Barlow

We propose to explore the potential of physics-informed neural networks (PINNs) in solving a class of partial differential equations (PDEs) used to model the propagation of chronic inflammatory bowel diseases, such as Crohn's disease and…

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

We consider solving the forward and inverse PDEs which have sharp solutions using physics-informed neural networks (PINNs) in this work. In particular, to better capture the sharpness of the solution, we propose adaptive sampling methods…

Numerical Analysis · Mathematics 2023-02-17 Zhiping Mao , Xuhui Meng

This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory…

Machine Learning · Computer Science 2025-12-10 Deepak Gupta , Himanshu Pandey , Ratikanta Behera

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Machine Learning · Computer Science 2024-07-18 Katsiaryna Haitsiukevich , Alexander Ilin

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

Numerical Analysis · Mathematics 2022-08-29 Antonio Tadeu Azevedo Gomes , Larissa Miguez da Silva , Frederic Valentin

Graph convolutional networks (GCNs) have emerged as a powerful alternative to multiple instance learning with convolutional neural networks in digital pathology, offering superior handling of structural information across various spatial…

Image and Video Processing · Electrical Eng. & Systems 2024-03-25 Victor Ibañez , Przemyslaw Szostak , Quincy Wong , Konstanty Korski , Samaneh Abbasi-Sureshjani , Alvaro Gomariz

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

Machine Learning · Computer Science 2022-12-16 Jian Cheng Wong , Chinchun Ooi , Abhishek Gupta , Yew-Soon Ong

Physics-informed neural networks (PINN) have recently emerged as a promising application of deep learning in a wide range of engineering and scientific problems based on partial differential equation (PDE) models. However, evidence shows…

Machine Learning · Computer Science 2022-10-24 Caio Davi , Ulisses Braga-Neto

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…

Machine Learning · Computer Science 2021-04-27 Mohammad Amin Nabian , Rini Jasmine Gladstone , Hadi Meidani

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Numerical Analysis · Mathematics 2023-05-23 Victorita Dolean , Alexander Heinlein , Siddhartha Mishra , Ben Moseley

We propose gradient-enhanced PINNs based on transfer learning (TL-gPINNs) for inverse problems of the function coefficient discovery in order to overcome deficiency of the discrete characterization of the PDE loss in neural networks and…

Numerical Analysis · Mathematics 2023-05-16 Shuning Lin , Yong Chen

Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…

Graphics · Computer Science 2026-05-27 Pranav Jain , Navami Kairanda , Peter Yichen Chen , Oded Stein

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Computational Physics · Physics 2026-03-25 Guoqiang Lei , D. Exposito , Xuerui Mao

The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by…

Machine Learning · Statistics 2025-12-30 Georgios Arampatzis , Stylianos Katsarakis , Charalambos Makridakis

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

Computational Engineering, Finance, and Science · Computer Science 2023-11-06 Chen Xu , Ba Trung Cao , Yong Yuan , Günther Meschke

Reaction-diffusion epidemic models with vital dynamics are an important framework for describing the spatial and temporal spread of infectious diseases. In this work, we present a constraint-aware, physics-informed neural network (PINN)…

Dynamical Systems · Mathematics 2026-05-20 Achraf Zinihi , Matthias Ehrhardt