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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

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Machine Learning · Computer Science 2022-08-09 Zhi-Yong Zhang , Hui Zhang , Li-Sheng Zhang , Lei-Lei Guo

We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical…

Machine Learning · Computer Science 2020-09-11 Enrui Zhang , Minglang Yin , George Em Karniadakis

Fractional physics-informed neural networks (fPINNs) have been successfully introduced in [Pang, Lu and Karniadakis, SIAM J. Sci. Comput. 41 (2019) A2603-A2626], which observe relative errors of $10^{-3} \, \sim \, 10^{-4}$ for the…

Numerical Analysis · Mathematics 2025-05-29 Na Xue , Minghua Chen

The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that automatic differentiation is not applicable for fractional…

Numerical Analysis · Mathematics 2023-04-04 Xiong-Bin Yan , Zhi-Qin John Xu , Zheng Ma

Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without…

Soft Condensed Matter · Physics 2025-11-07 Aditya Konale , Vikas Srivastava

Engineering components must meet increasing technological demands in ever shorter development cycles. To face these challenges, a holistic approach is essential that allows for the concurrent development of part design, material system and…

Machine Learning · Computer Science 2024-07-31 Tobias Würth , Niklas Freymuth , Clemens Zimmerling , Gerhard Neumann , Luise Kärger

Physics informed neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex problems as ones involving stiff ordinary differential…

Computational Physics · Physics 2023-04-18 Hubert Baty

Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including those with limited data availability. However, solving…

Machine Learning · Computer Science 2026-03-26 Himanshu Pandey , Anshima Singh , Ratikanta Behera

Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…

Machine Learning · Computer Science 2026-03-17 Aleksander Krasowski , René P. Klausen , Aycan Celik , Sebastian Lapuschkin , Wojciech Samek , Jonas Naujoks

How to solve inverse problems is the challenge of many engineering and industrial applications. Recently, physics-informed neural networks (PINNs) have emerged as a powerful approach to solve inverse problems efficiently. However, it is…

Numerical Analysis · Mathematics 2022-09-22 Xinchao Jiang , Xin Wanga , Ziming Wena , Enying Li , Hu Wang

I will demonstrate the effectiveness of Physics-Informed Neural Networks (PINNs) in solving partial differential equations (PDEs) when training data are scarce or noisy. The training data can be located either at the boundaries or within…

Solar and Stellar Astrophysics · Physics 2025-02-28 Hubert Baty

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

Machine Learning · Computer Science 2026-02-03 Olaf Yunus Laitinen Imanov

Structural failures are often caused by catastrophic events such as earthquakes and winds. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real time. Currently available high-fidelity…

Machine Learning · Computer Science 2022-11-30 Hamed Bolandi , Gautam Sreekumar , Xuyang Li , Nizar Lajnef , Vishnu Naresh Boddeti

We provide an approach enabling one to employ physics-informed neural networks (PINNs) for uncertainty quantification. Our approach is applicable to systems where observations are scarce (or even lacking), these being typical situations…

Data Analysis, Statistics and Probability · Physics 2024-08-12 Milad Panahi , Giovanni Michele Porta , Monica Riva , Alberto Guadagnini

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

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…

Numerical Analysis · Mathematics 2024-01-25 Vasiliy A. Es'kin , Danil V. Davydov , Julia V. Gur'eva , Alexey O. Malkhanov , Mikhail E. Smorkalov

Physics-informed neural networks (PINNs) have recently been used to solve various computational problems which are governed by partial differential equations (PDEs). In this paper, we propose a multi-output physics-informed neural network…

Computational Engineering, Finance, and Science · Computer Science 2022-12-07 Mingyuan Yang , John T. Foster

The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…

Fluid Dynamics · Physics 2021-05-25 Ryno Laubscher , Pieter Rousseau

In recent years, a plethora of methods combining deep neural networks and partial differential equations have been developed. A widely known and popular example are physics-informed neural networks. They solve forward and inverse problems…

Optimization and Control · Mathematics 2022-07-04 Bastian Zapf , Johannes Haubner , Miroslav Kuchta , Geir Ringstad , Per Kristian Eide , Kent-Andre Mardal