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Phase separation in binary mixtures, governed by the Cahn-Hilliard equation, plays a central role in interfacial dynamics across materials science and soft matter. While numerical solvers are accurate, they are often computationally…

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

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…

We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous…

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…

The objective of pansharpening and hypersharpening is to accurately combine a high-resolution panchromatic (PAN) image with a low-resolution multispectral (MS) or hyperspectral (HS) image, respectively. Unfolding fusion methods integrate…

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…

Recently, referring image segmentation has aroused widespread interest. Previous methods perform the multi-modal fusion between language and vision at the decoding side of the network. And, linguistic feature interacts with visual feature…

Recently, deploying deep neural network (DNN) models via collaborative inference, which splits a pre-trained model into two parts and executes them on user equipment (UE) and edge server respectively, becomes attractive. However, the large…

High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets'…

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural…

Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential…

We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly…

Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

Solutions to many partial differential equations (PDEs) display coexisting smooth global transport and localized sharp features within a single trajectory: shock fronts, thin interfaces, and concentrated high-frequency content sit on top of…

Density functional theory (DFT) is a cornerstone of computational chemistry and materials science, but its computational cost limits its use in large-scale and high-throughput applications. While machine learning has accelerated energy…

Infrared and visible image fusion, as a hot topic in image processing and image enhancement, aims to produce fused images retaining the detail texture information in visible images and the thermal radiation information in infrared images. A…

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…