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Related papers: PPINN: Parareal Physics-Informed Neural Network fo…

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Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

Machine Learning · Computer Science 2021-11-12 Aditi S. Krishnapriyan , Amir Gholami , Shandian Zhe , Robert M. Kirby , Michael W. Mahoney

Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, Extended PINNs…

Machine Learning · Computer Science 2022-10-19 Zheyuan Hu , Ameya D. Jagtap , George Em Karniadakis , Kenji Kawaguchi

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…

Machine Learning · Statistics 2024-04-03 Zhikang Dong , Pawel Polak

Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…

Computational Engineering, Finance, and Science · Computer Science 2024-08-23 Saakaar Bhatnagar , Andrew Comerford , Araz Banaeizadeh

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

Physics-Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only…

Machine Learning · Computer Science 2022-10-25 Jia Guo , Haifeng Wang , Chenping Hou

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

Recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network, such that the network not only conforms to…

Numerical Analysis · Mathematics 2021-11-17 Weiqi Ji , Weilun Qiu , Zhiyu Shi , Shaowu Pan , Sili Deng

Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Based on…

Machine Learning · Computer Science 2026-02-05 Tianchi Yu , Ivan Oseledets

Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover…

Machine Learning · Computer Science 2026-05-06 Zhao Wei , Kenneth Hor Cheng Koh , Sheng Yuan Chin , James Chun Yip Chan , Chin Chun Ooi , Yew-Soon Ong

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Machine Learning · Computer Science 2022-01-31 Pu Ren , Chengping Rao , Yang Liu , Jianxun Wang , Hao Sun

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…

Machine Learning · Computer Science 2026-03-25 Tetsuro Tsuchino , Motoki Shiga

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

Numerical Analysis · Mathematics 2024-11-28 Marco Berardi , Fabio Difonzo , Matteo Icardi

We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of…

Machine Learning · Computer Science 2020-12-07 Jungeun Kim , Kookjin Lee , Dongeun Lee , Sheo Yon Jin , Noseong Park

Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in…

Machine Learning · Computer Science 2022-05-19 Wensheng Li , Chao Zhang , Chuncheng Wang , Hanting Guan , Dacheng Tao

Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…

Numerical Analysis · Mathematics 2023-12-07 Siddhartha Mishra , Roberto Molinaro

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

Computational Physics · Physics 2022-05-24 Shamsulhaq Basir , Inanc Senocak

In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the…

Computational Physics · Physics 2025-10-31 Ehsan Ghaderi , Mohamad Ali Bijarchi , Siamak Kazemzadeh Hannani , Ali Nouri Boroujerdi

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…

Fluid Dynamics · Physics 2024-02-28 Rahul Sundar , Dipanjan Majumdar , Didier Lucor , Sunetra Sarkar

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…

Machine Learning · Statistics 2023-10-09 Inbar Seroussi , Asaf Miron , Zohar Ringel