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Fourier Neural Operator (FNO) is a popular operator learning framework. It not only achieves the state-of-the-art performance in many tasks, but also is efficient in training and prediction. However, collecting training data for the FNO can…

Machine Learning · Computer Science 2024-04-01 Shibo Li , Xin Yu , Wei Xing , Mike Kirby , Akil Narayan , Shandian Zhe

Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…

Machine Learning · Computer Science 2025-05-08 Shuhao Cao , Francesco Brarda , Ruipeng Li , Yuanzhe Xi

The inception of spatial transcriptomics has allowed improved comprehension of tissue architectures and the disentanglement of complex underlying biological, physiological, and pathological processes through their positional contexts.…

Machine Learning · Computer Science 2023-02-02 Junaid Ahmed , Alhassan S. Yasin

Neural operators have been validated as promising deep surrogate models for solving partial differential equations (PDEs). Despite the critical role of boundary conditions in PDEs, however, only a limited number of neural operators robustly…

Numerical Analysis · Mathematics 2023-12-13 Ziyuan Liu , Yuhang Wu , Daniel Zhengyu Huang , Hong Zhang , Xu Qian , Songhe Song

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…

Most dimensionality reduction methods treat data as discrete point clouds, ignoring the continuous domain structure inherent to many real-world processes. To bridge this gap, we introduce Neural Operator Function Embedding (NOFE), a…

A standard practice in developing image recognition models is to train a model on a specific image resolution and then deploy it. However, in real-world inference, models often encounter images different from the training sets in resolution…

Computer Vision and Pattern Recognition · Computer Science 2024-03-15 Jinsung Jeon , Hyundong Jin , Jonghyun Choi , Sanghyun Hong , Dongeun Lee , Kookjin Lee , Noseong Park

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…

Numerical Analysis · Mathematics 2023-10-31 Zecheng Zhang , Christian Moya , Lu Lu , Guang Lin , Hayden Schaeffer

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

Pansharpening aims to synthesize high-resolution multispectral (HR-MS) images by fusing the spatial textures of panchromatic (PAN) images with the spectral information of low-resolution multispectral (LR-MS) images. While recent deep…

Computer Vision and Pattern Recognition · Computer Science 2026-04-15 Anqi Zhu , Mengting Ma , Yizhen Jiang , Xiangdong Li , Kai Zheng , Jiaxin Li , Wei Zhang

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…

Machine Learning · Computer Science 2025-05-28 Zaijun Ye , Chen-Song Zhang , Wansheng Wang

Neural operators provide fast surrogate models for time-dependent partial differential equations, but their standard autoregressive use usually assumes that the instantaneous field $u(t,\cdot)$ is a complete state. This assumption fails for…

Machine Learning · Computer Science 2026-05-13 Lennon J. Shikhman

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

Multiphase flow simulation is critical in science and engineering but incurs high computational costs due to complex field discontinuities and the need for high-resolution numerical meshes. While Neural Operators (NOs) offer an efficient…

Fluid Dynamics · Physics 2025-12-04 Zhenzhong Wang , Xin Zhang , Jun Liao , Min Jiang

Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they…

Optimization and Control · Mathematics 2026-03-02 Takashi Furuya , Anastasis Kratsios

This paper introduces HyperNOs, a PyTorch library designed to streamline and automate the process of exploring neural operators, with a special focus on hyperparameter optimization for comprehensive and exhaustive exploration. Indeed,…

Machine Learning · Computer Science 2026-02-09 Massimiliano Ghiotto

Exploring the outer atmosphere of the sun has remained a significant bottleneck in astrophysics, given the intricate magnetic formations that significantly influence diverse solar events. Magnetohydrodynamics (MHD) simulations allow us to…

Solar and Stellar Astrophysics · Physics 2024-09-10 Yutao Du , Qin Li , Raghav Gnanasambandam , Mengnan Du , Haimin Wang , Bo Shen

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

We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model evaluations are computationally expensive. We present a…

Machine Learning · Computer Science 2026-04-02 Josephine Westermann , Benno Huber , Thomas O'Leary-Roseberry , Jakob Zech

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…

Machine Learning · Computer Science 2023-05-17 Min Zhu , Handi Zhang , Anran Jiao , George Em Karniadakis , Lu Lu