Related papers: Adaptive Fourier Neural Operators: Efficient Token…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness. However, FNO is observed to be ineffective with large Fourier kernels that parameterize more frequencies. Current…

Recent advances in transformer-based models have drawn attention to exploring these techniques in medical image segmentation, especially in conjunction with the U-Net model (or its variants), which has shown great success in medical image…

Magnetotelluric (MT) forward modeling is fundamental for improving the accuracy and efficiency of MT inversion. Neural operators (NOs) have been effectively used for rapid MT forward modeling, demonstrating their promising performance in…

Various factorization-based methods have been proposed to leverage second-order, or higher-order cross features for boosting the performance of predictive models. They generally enumerate all the cross features under a predefined maximum…

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…

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

Extensive work has demonstrated the effectiveness of Vision Transformers. The plain Vision Transformer tends to obtain multi-scale features by selecting fixed layers, or the last layer of features aiming to achieve higher performance in…

We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…

Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those originating from partial differential equations. Such characteristics render them an effective approach for simulating the time evolution of quantum…

The numerical approximation of the Boltzmann collision operator presents significant challenges arising from its high dimensionality, nonlinear structure, and nonlocal integral form. In this work, we propose a Fourier Neural Operator (FNO)…

Multi-head-self-attention (MHSA)-equipped models have achieved notable performance in computer vision. Their computational complexity is proportional to quadratic numbers of pixels in input feature maps, resulting in slow processing,…

Existing semantic segmentation works have been mainly focused on designing effective decoders; however, the computational load introduced by the overall structure has long been ignored, which hinders their applications on…

Vision transformer based models bring significant improvements for image segmentation tasks. Although these architectures offer powerful capabilities irrespective of specific segmentation tasks, their use of computational resources can be…

Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D…

Existing stereo matching networks typically rely on either cost-volume construction based on 3D convolutions or deformation methods based on iterative optimization. The former incurs significant computational overhead during cost…

The great success of Deep Neural Networks (DNNs) has inspired the algorithmic development of DNN-based Fixed-Point (DNN-FP) for computer vision tasks. DNN-FP methods, trained by Back-Propagation Through Time or computing the inaccurate…

Convolutional Neural Networks (CNNs) and Transformers have achieved remarkable success in computer vision tasks. However, their deep architectures often lead to high computational redundancy, making them less suitable for…

Window-based transformers have demonstrated outstanding performance in super-resolution tasks due to their adaptive modeling capabilities through local self-attention (SA). However, they exhibit higher computational complexity and inference…

Deep learning methods are emerging as popular computational tools for solving forward and inverse problems in traffic flow. In this paper, we study a neural operator framework for learning solutions to nonlinear hyperbolic partial…