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Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…

Solving partial differential equations (PDEs) is an important research means in the fields of physics, biology, and chemistry. As an approximate alternative to numerical methods, PINN has received extensive attention and played an important…

Estimating redshift is a central task in astrophysics, but its measurement is costly and time-consuming. In addition, current image-based methods are often validated on homogeneous datasets. The development and comparison of networks able…

Recent advanced studies have spent considerable human efforts on optimizing network architectures for stereo matching but hardly achieved both high accuracy and fast inference speed. To ease the workload in network design, neural…

The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…

We introduce a continuous depth version of the Residual Network (ResNet) called Neural ordinary differential equations (NODE) for the purpose of galaxy morphology classification. We carry out a classification of galaxy images from the…

This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the computational cost using traditional numerical schemes can be…

Background: Deep learning techniques, particularly neural networks, have revolutionized computational physics, offering powerful tools for solving complex partial differential equations (PDEs). However, ensuring stability and efficiency…

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…

A residual network (or ResNet) is a standard deep neural net architecture, with state-of-the-art performance across numerous applications. The main premise of ResNets is that they allow the training of each layer to focus on fitting just…

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…

Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…

Machine learning methods for solving nonlinear partial differential equations (PDEs) are hot topical issues, and different algorithms proposed in the literature show efficient numerical approximation in high dimension. In this paper, we…

The structural analogies of ResNets and Multigrid (MG) methods such as common building blocks like convolutions and poolings where already pointed out by He et al.\ in 2016. Multigrid methods are used in the context of scientific computing…

Modern computer vision architectures, from CNNs to Transformers, predominantly rely on the stacking of heuristic modules: spatial mixers (Attention/Conv) followed by channel mixers (FFNs). In this work, we challenge this paradigm by…

In the stereo matching task, matching cost aggregation is crucial in both traditional methods and deep neural network models in order to accurately estimate disparities. We propose two novel neural net layers, aimed at capturing local and…

This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs). Given the property of smoothing iterations in multigrid methods where…

In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…