Related papers: Adaptive Fourier Neural Operators: Efficient Token…

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…

Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as…

Neural operators have emerged as a powerful, data-driven paradigm for learning solution operators of partial differential equations (PDEs). State-of-the-art architectures, such as the Fourier Neural Operator (FNO), have achieved remarkable…

Transformer-based language models utilize the attention mechanism for substantial performance improvements in almost all natural language processing (NLP) tasks. Similar attention structures are also extensively studied in several other…

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…

In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs). Neural operators are a discretization-invariant generalization of neural…

We present Token-UNet, adopting the TokenLearner and TokenFuser modules to encase Transformers into UNets. While Transformers have enabled global interactions among input elements in medical imaging, current computational challenges hinder…

This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that…

Efficient and accurate time-domain simulation of electromagnetic fields in complex photonic devices is critical for designing broadband and ultrafast optical components, yet it is often limited by the high computational cost of conventional…

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…

Modeling high-frequency information is a critical challenge in scientific machine learning. For instance, fully turbulent flow simulations of the Navier-Stokes equations at Reynolds numbers 3500 and above can generate high-frequency signals…

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

Meta-optics promises compact, high-performance imaging and color routing. However, designing high-performance structures is a high-dimensional optimization problem: mapping a desired optical output back to a physical 3D structure requires…

Due to the computational complexity of 3D medical image segmentation, training with downsampled images is a common remedy for out-of-memory errors in deep learning. Nevertheless, as standard spatial convolution is sensitive to variations in…

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…

Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…

Neural operators are a new type of models that can map between function spaces, allowing trained models to emulate the solution operators of partial differential equations (PDEs). This paper proposes a multigrid Fourier neural operator…

Lensless cameras based on thin diffusers offer a compact alternative to conventional refractive imaging but rely on computational reconstruction, since the diffuser's point spread function (PSF) globally multiplexes every scene point across…

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…