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Related papers: PAC-FNO: Parallel-Structured All-Component Fourier…

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Fourier ptychography is a recently developed imaging approach for large field-of-view and high-resolution microscopy. Here we model the Fourier ptychographic forward imaging process using a convolution neural network (CNN) and recover the…

Computer Vision and Pattern Recognition · Computer Science 2018-03-12 Shaowei Jiang , Kaikai Guo , Jun Liao , Guoan Zheng

Deep learning methods are emerging as popular computational tools for solving forward and inverse problems in traffic flow. In this paper, we study a neural operator framework for learning solutions to nonlinear hyperbolic partial…

Machine Learning · Computer Science 2024-06-26 Bilal Thonnam Thodi , Sai Venkata Ramana Ambadipudi , Saif Eddin Jabari

One of the fundamental challenges in image restoration is denoising, where the objective is to estimate the clean image from its noisy measurements. To tackle such an ill-posed inverse problem, the existing denoising approaches generally…

Computer Vision and Pattern Recognition · Computer Science 2021-11-12 Lanqing Guo , Siyu Huang , Haosen Liu , Bihan Wen

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

High-fidelity simulations of laser welding capture complex thermo-fluid phenomena, including phase change, free-surface deformation, and keyhole dynamics, however their computational cost limits large-scale process exploration and real-time…

Machine Learning · Computer Science 2026-04-01 Alix Benoit , Toni Ivas , Mateusz Papierz , Asel Sagingalieva , Alexey Melnikov , Elia Iseli

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…

Machine Learning · Computer Science 2025-02-24 Qinglong Ma , Peizhi Zhao , Sen Wang , Tao Song

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

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In…

Machine Learning · Computer Science 2023-07-25 Hongkai Zheng , Weili Nie , Arash Vahdat , Kamyar Azizzadenesheli , Anima Anandkumar

Efficient onboard multi-field sparse reconstruction is essential for the autonomous operation of aerospace vehicles. While existing deep learning models exhibit promise for single-field reconstruction, deploying multiple independent models…

Machine Learning · Computer Science 2026-05-27 Siyu Ye , Shihang Li , Zhiqiang Gong , Benrong Zhang , Weien Zhou , Yiyong Huang , Wen Yao

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…

Fluid Dynamics · Physics 2025-11-04 Marco Cayuela , Vincent Le Chenadec , Peter Schmid , Taraneh Sayadi

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that…

Machine Learning · Computer Science 2024-06-11 Miguel Liu-Schiaffini , Julius Berner , Boris Bonev , Thorsten Kurth , Kamyar Azizzadenesheli , Anima Anandkumar

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness. However, FNO is observed to be ineffective with large Fourier kernels that parameterize more frequencies. Current…

Machine Learning · Computer Science 2024-10-10 Shaoxiang Qin , Fuyuan Lyu , Wenhui Peng , Dingyang Geng , Ju Wang , Xing Tang , Sylvie Leroyer , Naiping Gao , Xue Liu , Liangzhu Leon Wang

This study aims to develop surrogate models for accelerating decision making processes associated with carbon capture and storage (CCS) technologies. Selection of sub-surface $CO_2$ storage sites often necessitates expensive and involved…

Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation…

Artificial Intelligence · Computer Science 2023-02-21 Xiaoyu Zhao , Xiaoqian Chen , Zhiqiang Gong , Weien Zhou , Wen Yao , Yunyang Zhang

In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Building on the structure of Fourier Neural Operators (FNO),…

Numerical Analysis · Mathematics 2025-04-28 Zilan Cheng , Zhongjian Wang , Li-Lian Wang , Mejdi Azaiez

Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave…

Atmospheric and Oceanic Physics · Physics 2024-01-11 Svenja Ehlers , Marco Klein , Alexander Heinlein , Mathies Wedler , Nicolas Desmars , Norbert Hoffmann , Merten Stender

Unsupervised image registration commonly adopts U-Net style networks to predict dense displacement fields in the full-resolution spatial domain. For high-resolution volumetric image data, this process is however resource-intensive and…

Computer Vision and Pattern Recognition · Computer Science 2023-07-07 Xi Jia , Joseph Bartlett , Wei Chen , Siyang Song , Tianyang Zhang , Xinxing Cheng , Wenqi Lu , Zhaowen Qiu , Jinming Duan

Neural networks are one of the disruptive computing concepts of our time. However, they fundamentally differ from classical, algorithmic computing in a number of fundamental aspects. These differences result in equally fundamental, severe…

Neural and Evolutionary Computing · Computer Science 2020-12-22 Xavier Porte , Anas Skalli , Nasibeh Haghighi , Stephan Reitzenstein , James A. Lott , Daniel Brunner

We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit…

Machine Learning · Computer Science 2023-05-31 Qianying Cao , Somdatta Goswami , George Em Karniadakis

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

Quantum Physics · Physics 2025-09-10 Zihao Qi , Yang Peng , Christopher Earls