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The rise of Physics-Informed Neural Networks (PINNs) has popularized the concept of solving differential equations via residual minimization. However, neural networks are often viewed as ``black boxes" requiring significant computational…

Numerical Analysis · Mathematics 2026-05-20 Ayman Mourad , Fatima Mroue

In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional…

Fluid Dynamics · Physics 2026-01-05 Xuehui Qian , Hongkai Tao , Yongji Wang

Physics-informed neural networks (PINNs) are neural networks that embed the laws of dynamical systems modeled by differential equations into their loss function as constraints. In this work, we present a PINN framework applied to oncology.…

Machine Learning · Computer Science 2025-10-16 Kayode Olumoyin , Katarzyna Rejniak

We introduce Nonlinear GENERIC Informed Neural Networks (N-GINNs), a deep learning framework for discovering evolution equations of systems governed by the nonlinear GENERIC formalism (General Equation for Non-Equilibrium…

Computational Physics · Physics 2026-05-12 Vojtěch Votruba , Zequn He , Weilun Qiu , Celia Reina , Michal Pavelka

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the…

Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…

Machine Learning · Statistics 2026-04-10 Brenda Anague , Bamdad Hosseini , Issa Karambal , Jean Medard Ngnotchouye

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…

Machine Learning · Computer Science 2023-01-16 Ulisses Braga-Neto

In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful…

Machine Learning · Computer Science 2025-08-27 Jason Matthews , Alex Bihlo

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…

Computational Physics · Physics 2024-06-21 Ben Moseley , Andrew Markham , Tarje Nissen-Meyer

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…

Machine Learning · Computer Science 2024-01-11 Haoyu Chu , Yuto Miyatake , Wenjun Cui , Shikui Wei , Daisuke Furihata

Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…

Robotics · Computer Science 2024-11-05 Youngsun Wi , Jayjun Lee , Miquel Oller , Nima Fazeli

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…

Machine Learning · Computer Science 2021-11-03 Lu Lu , Xuhui Meng , Zhiping Mao , George E. Karniadakis

We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the…

Machine Learning · Computer Science 2025-03-11 Zongren Zou , Zhicheng Wang , George Em Karniadakis

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…

Numerical Analysis · Mathematics 2023-02-09 Pongpisit Thanasutives , Takashi Morita , Masayuki Numao , Ken-ichi Fukui

In this work, a physics-informed neural networks (PINNs) based algorithm is used for simulation of nonlinear 1D and 2D Burgers' type models. This scheme relies on a neural network built to approximate the problem solution and use a trial…

Machine Learning · Computer Science 2025-06-17 Ajeet Singh , Ram Jiwari , Vikram , Ujjwal Saini

Contraction analysis offers, through elegant mathematical developments, a unified way of designing observers for a general class of nonlinear systems, where the observer correction term is obtained by solving an infinite dimensional…

Systems and Control · Electrical Eng. & Systems 2024-11-15 Yasmine Marani , Israel Filho , Tareq Al-Naffouri , Taous-Meriem Laleg-Kirati

Nonlinear system identification must balance physical interpretability with model flexibility. Classical methods yield structured, control-relevant models but rely on rigid parametric forms that often miss complex nonlinearities, whereas…

Machine Learning · Computer Science 2026-04-17 Murat Furkan Mansur , Tufan Kumbasar

Physics-informed neural networks (PINNs), owing to their mesh-free nature, offer a powerful approach for solving high-dimensional partial differential equations (PDEs) in complex geometries, including irregular domains. This capability…

Numerical Analysis · Mathematics 2025-06-06 Hanfei Zhou , Lei Shi

In this paper, we introduce a new deep learning framework for discovering the phase field models from existing image data. The new framework embraces the approximation power of physics informed neural networks (PINN), and the computational…

Numerical Analysis · Mathematics 2020-07-10 Jia Zhao

Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…

Fluid Dynamics · Physics 2025-04-01 Yongzheng Zhu , Weizheng Chen , Jian Deng , Xin Bian
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