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In this study, we investigate the capability of physics-informed neural networks (PINNs) to preserve global physical structures by comparing standard PINNs with a Trefftz-based PINN (Trefftz-PINN). The target problem is the reproduction of…

Numerical Analysis · Mathematics 2026-05-07 Koji Koyamada

Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs), particularly in regimes where labeled data are scarce and physical constraints can be…

Machine Learning · Computer Science 2026-02-12 Nicolás Becerra-Zuniga , Lucas Lacasa , Eusebio Valero , Gonzalo Rubio

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric…

Machine Learning · Computer Science 2025-05-02 Júlia Vicens Figueres , Juliette Vanderhaeghen , Federica Bragone , Kateryna Morozovska , Khemraj Shukla

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

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…

Machine Learning · Computer Science 2023-06-19 Junjun Yan , Xinhai Chen , Zhichao Wang , Enqiang Zhoui , Jie Liu

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…

Numerical Analysis · Mathematics 2024-07-30 Hamed Saidaoui , Luis Espath , Rául Tempone

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…

Machine Learning · Computer Science 2026-01-29 Chen-Yang Dai , Che-Chia Chang , Te-Sheng Lin , Ming-Chih Lai , Chieh-Hsin Lai

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

Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the…

Computational Engineering, Finance, and Science · Computer Science 2025-06-16 Stefan Schoder , Aneta Furmanová , Viktor Hruška

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…

Machine Learning · Computer Science 2023-05-26 Jia Sun , Yinghua Liu , Yizheng Wang , Zhenhan Yao , Xiaoping Zheng

The computation of the seismic wavefield by solving the Helmholtz equation is crucial to many practical applications, e.g., full waveform inversion. Physics-informed neural networks (PINNs) provide functional wavefield solutions represented…

Geophysics · Physics 2024-08-29 Xinquan Huang , Tariq Alkhalifah

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

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

Machine Learning · Computer Science 2023-05-08 Chandrajit Bajaj , Luke McLennan , Timothy Andeen , Avik Roy

Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of…

Numerical Analysis · Mathematics 2025-12-18 Conor Rowan , Kai Hampleman , Kurt Maute , Alireza Doostan

In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic…

Exactly Solvable and Integrable Systems · Physics 2022-01-26 Zhengwu Miao , Yong Chen

We present a Physics-Informed Neural Network (PINN) framework for reconstructing the redshift-dependent Hubble parameter \(H(z)\) within the Tsallis Holographic Dark Energy (THDE) model extended by massive neutrinos. In this approach, the…

Cosmology and Nongalactic Astrophysics · Physics 2025-11-14 Muhammad Yarahmadi , Amin Salehi

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

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…

Machine Learning · Computer Science 2026-05-08 Reza Pirayeshshirazinezhad

Physics-informed neural networks (PINNs) employed in fluid mechanics deal primarily with stationary boundaries. This hinders the capability to address a wide range of flow problems involving moving bodies. To this end, we propose a novel…

Fluid Dynamics · Physics 2025-08-05 Yongzheng Zhu , Weizhen Kong , Jian Deng , Xin Bian

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