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In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the…

Numerical Analysis · Mathematics 2024-12-31 Zhilin You , Zhenli Xu , Wei Cai

Long-term prediction of three-dimensional (3D) turbulent flows is one of the most challenging problems for machine learning approaches. Although some existing machine learning approaches such as implicit U-net enhanced Fourier neural…

Fluid Dynamics · Physics 2025-11-04 Yuchi Jiang , Zhijie Li , Yunpeng Wang , Huiyu Yang , Jianchun Wang

Transformers have become the de facto standard for a wide range of tasks, from image classification to physics simulations. Despite their impressive performance, the quadratic complexity of standard Transformers in both memory and time with…

Computer Vision and Pattern Recognition · Computer Science 2025-07-04 Alex Colagrande , Paul Caillon , Eva Feillet , Alexandre Allauzen

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Machine Learning · Computer Science 2025-04-30 W. Diab , M. Al-Kobaisi

This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…

Machine Learning · Computer Science 2025-10-21 Daniil D. Sirota , Sergey A. Khan , Sergey L. Kostikov , Kirill A. Butov

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

Machine Learning · Computer Science 2026-05-11 Vasilis Niarchos , Angelos Sirbu , Sokratis Trifinopoulos

The UNet-enhanced Fourier Neural Operator (UFNO) extends the Fourier Neural Operator (FNO) by incorporating a parallel UNet pathway, enabling the retention of both high- and low-frequency components. While UFNO improves predictive accuracy…

Machine Learning · Computer Science 2026-01-05 Alhasan Abdellatif , Hannah P. Menke , Florian Doster , Kamaljit Singh , Ahmed H. Elsheikh

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…

Machine Learning · Computer Science 2023-10-13 Karn Tiwari , N M Anoop Krishnan , Prathosh A P

The full-duplex (FD) communication can achieve higher spectrum efficiency than conventional half-duplex (HD) communication; however, self-interference (SI) is the key hurdle. This paper is the first work to propose the intelligent Omni…

Information Theory · Computer Science 2022-08-22 Sisai Fang , Gaojie Chen , Pei Xiao , Kai-Kit Wong , Rahim Tafazolli

Neural operators are a new type of models that can map between function spaces, allowing trained models to emulate the solution operators of partial differential equations (PDEs). This paper proposes a multigrid Fourier neural operator…

Numerical Analysis · Mathematics 2025-05-22 Zi-Hao Guo , Hou-Biao Li

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…

A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For…

Numerical Analysis · Mathematics 2024-04-02 V. Fanaskov , I. Oseledets

Fourier Neural Operators (FNOs) have emerged as promising surrogates for partial differential equation solvers. In this work, we extensively tested FNOs on a variety of systems with non-linear and non-stationary properties, using a wide…

Computational Engineering, Finance, and Science · Computer Science 2025-11-13 Rad Haghi , Bipin Gaikwad , Abani Patra

Numerical simulations are essential tools to evaluate the solution of the wave equation in complex settings, such as three-dimensional (3D) domains with heterogeneous properties. However, their application is limited by high computational…

Machine Learning · Computer Science 2025-04-09 Fanny Lehmann , Filippo Gatti , Didier Clouteau

Accurate real-time prediction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation methods for reconstructing initial conditions from sparse or…

Machine Learning · Computer Science 2025-08-06 Svenja Ehlers , Merten Stender , Norbert Hoffmann

Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…

Machine Learning · Computer Science 2024-11-12 Conlain Kelly , Surya R. Kalidindi

Neural operators offer a powerful data-driven framework for learning mappings between function spaces, in which the transformer-based neural operator architecture faces a fundamental scalability-accuracy trade-off: softmax attention…

Machine Learning · Computer Science 2025-10-21 Ming Zhong , Zhenya Yan

Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While…

Machine Learning · Computer Science 2025-10-30 Yaozhong Shi , Zachary E. Ross , Domniki Asimaki , Kamyar Azizzadenesheli

Flexible intelligent metasurfaces (FIMs) offer a new solution for wireless communications by introducing morphological degrees of freedom, dynamically morphing their three-dimensional shape to ensure multipath signals interfere…

Information Theory · Computer Science 2026-04-08 Jian Xiao , Ji Wang , Qimei Cui , Yucang Yang , Xingwang Li , Dusit Niyato , Chau Yuen

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper,…