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In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

In multi-body dynamics, the motion of a complicated physical object is described as a coupled ordinary differential equation system with multiple unknown solutions. Engineers need to constantly adjust the object to meet requirements at the…

Computational Engineering, Finance, and Science · Computer Science 2022-05-26 Wenhao Ding , Qing He , Hanghang Tong , Ping Wang

Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To…

Machine Learning · Computer Science 2024-12-02 Honghui Wang , Yifan Pu , Shiji Song , Gao Huang

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

Computational Physics · Physics 2026-03-27 Q. C. Dong , Zi-Xuan Su , Qing Huo Liu , Wen Chen , Zhizhang , Chen

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data…

Machine Learning · Computer Science 2026-02-16 Heechang Kim , Qianying Cao , Hyomin Shin , Seungchul Lee , George Em Karniadakis , Minseok Choi

Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to…

Machine Learning · Computer Science 2026-04-22 Hannah Lydon , Milad Kazemi , Martin Bishop , Nicola Paoletti

As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…

Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly…

Machine Learning · Computer Science 2024-11-14 Weiheng Zhong , Hadi Meidani

The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…

Machine Learning · Computer Science 2025-10-29 Sumanta Roy , Bahador Bahmani , Ioannis G. Kevrekidis , Michael D. Shields

Solving Partial Differential Equations (PDEs) is the core of many fields of science and engineering. While classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information.…

Machine Learning · Computer Science 2024-02-13 Cooper Lorsung , Zijie Li , Amir Barati Farimani

Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into…

Neural and Evolutionary Computing · Computer Science 2023-07-11 Bo Wang , A. K. Qin , Sajjad Shafiei , Hussein Dia , Adriana-Simona Mihaita , Hanna Grzybowska

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

Machine Learning · Computer Science 2025-02-28 Biao Yuan , He Wang , Yanjie Song , Ana Heitor , Xiaohui Chen

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Machine Learning · Computer Science 2025-11-06 Gang Bao , Yaohua Zang

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

Machine Learning · Computer Science 2026-03-11 Nanxi Chen , Airong Chen , Rujin Ma

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…

Machine Learning · Computer Science 2025-06-24 Jing Wang , Biao Chen , Hairun Xie , Rui Wang , Yifan Xia , Jifa Zhang , Hui Xu

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…

Fluid Dynamics · Physics 2025-11-19 Ritik Pal , Soubhik Mukherjee , Urmi Dutta , Arghya Choudhury

Self-training techniques have shown remarkable value across many deep learning models and tasks. However, such techniques remain largely unexplored when considered in the context of learning fast solvers for systems of partial differential…

Machine Learning · Computer Science 2023-11-27 Ritam Majumdar , Amey Varhade , Shirish Karande , Lovekesh Vig

Wave propagation problems are typically formulated as partial differential equations (PDEs) on unbounded domains to be solved. The classical approach to solving such problems involves truncating them to problems on bounded domains by…

Numerical Analysis · Mathematics 2024-04-11 Jihong Wang , Xin Wang , Jing Li , Bin Liu
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