Related papers: PeSANet: Physics-encoded Spectral Attention Networ…

Semantic segmentation stands as a pivotal research focus in computer vision. In the context of industrial image inspection, conventional semantic segmentation models fail to maintain the segmentation consistency of fixed components across…

Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Long-term time series forecasting (LTSF) is hampered by the challenge of modeling complex dependencies that span multiple temporal scales and frequency resolutions. Existing methods, including Transformer and MLP-based models, often…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

We consider the problem of segmentation and classification of high-resolution and hyperspectral remote sensing images. Unlike conventional natural (RGB) images, the inherent large scale and complex structures of remote sensing images pose…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Deep Operator Networks (DeepONets) have become a central tool in data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk design based…

We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely…

Spatial attention mechanism has been widely used in semantic segmentation of remote sensing images given its capability to model long-range dependencies. Many methods adopting spatial attention mechanism aggregate contextual information…

Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations. Despite their promising…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

The increase of available large clinical and experimental datasets has contributed to a substantial amount of important contributions in the area of biomedical image analysis. Image segmentation, which is crucial for any quantitative…

Leveraging physical knowledge described by partial differential equations (PDEs) is an appealing way to improve unsupervised video prediction methods. Since physics is too restrictive for describing the full visual content of generic…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

This research introduces the Theory of Partial Symmetry Enforced Attention Decomposition (PSEAD), a new and rigorous group-theoretic framework designed to seamlessly integrate local symmetry awareness into the core architecture of…

Medical image segmentation, particularly in multi-domain scenarios, requires precise preservation of anatomical structures across diverse representations. While deep learning has advanced this field, existing models often struggle with…