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Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Machine Learning · Computer Science 2026-04-16 Kentaro Hoshisashi , Carolyn E Phelan , Paolo Barucca

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into…

Dynamical Systems · Mathematics 2023-12-19 Xi'an Li , Jiaxin Deng , Jinran Wu , Shaotong Zhang , Weide Li , You-Gan Wang

Physics-Informed Neural Networks (PINNs) have become a prominent application of deep learning in scientific computation, as they are powerful approximators of solutions to nonlinear partial differential equations (PDEs). There have been…

Machine Learning · Computer Science 2023-06-01 Hwijae Son , Sung Woong Cho , Hyung Ju Hwang

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…

Numerical Analysis · Mathematics 2024-07-15 Seungchan Ko , Sang Hyeon Park

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

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 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

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…

Machine Learning · Statistics 2019-07-08 Somdatta Goswami , Cosmin Anitescu , Souvik Chakraborty , Timon Rabczuk

Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network, and this PDE loss is…

Computational Physics · Physics 2023-07-19 Chenxi Wu , Min Zhu , Qinyang Tan , Yadhu Kartha , Lu Lu

Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs often struggle to learn high-frequency and multi-scale…

Machine Learning · Computer Science 2025-02-25 Madison Cooley , Varun Shankar , Robert M. Kirby , Shandian Zhe

Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. PINNs integrate the physical constraints by minimizing the…

Machine Learning · Computer Science 2025-07-28 Thi Nguyen Khoa Nguyen , Thibault Dairay , Raphaël Meunier , Christophe Millet , Mathilde Mougeot

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, their performance heavily relies on the strategy used to select training points. Conventional adaptive…

Machine Learning · Computer Science 2025-04-18 Zhenao Song

We propose to enhance the training of physics-informed neural networks (PINNs). To this aim, we introduce nonlinear additive and multiplicative preconditioning strategies for the widely used L-BFGS optimizer. The nonlinear preconditioners…

Numerical Analysis · Mathematics 2024-04-16 Alena Kopaničáková , Hardik Kothari , George Em Karniadakis , Rolf Krause

We propose a hybrid framework opPINN: physics-informed neural network (PINN) with operator learning for approximating the solution to the Fokker-Planck-Landau (FPL) equation. The opPINN framework is divided into two steps: Step 1 and Step…

Numerical Analysis · Mathematics 2023-03-22 Jae Yong Lee , Juhi Jang , Hyung Ju Hwang

Integration of machine learning (ML) into the topology optimization (TO) framework is attracting increasing attention, but data acquisition in data-driven models is prohibitive. Compared with popular ML methods, the physics-informed neural…

Machine Learning · Computer Science 2023-12-13 Jichao Yin , Ziming Wen , Shuhao Li , Yaya Zhanga , Hu Wang

In this paper, we develop a deep learning approach for the accurate solution of challenging problems of near-field microscopy that leverages the powerful framework of physics-informed neural networks (PINNs) for the inversion of the complex…

Optics · Physics 2024-06-12 Yuyao Chen , Luca Dal Negro

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…

Machine Learning · Computer Science 2019-07-09 Vikas Dwivedi , Balaji Srinivasan

This paper presents eXtended Physics-Informed Neural Network (X-PINN), a novel and robust framework for addressing fracture mechanics problems involving multiple cracks in fractured media. To address this, an energy-based loss function,…

Machine Learning · Computer Science 2025-09-18 Amin Lotfalian , Mohammad Reza Banan , Pooyan Broumand

Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization…

Machine Learning · Computer Science 2026-04-07 Yongsheng Chen , Yong Chen , Wei Guo , Xinghui Zhong

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

Machine Learning · Computer Science 2023-06-21 Shamsulhaq Basir