相关论文: Spectral Neural Operators

Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures…

We introduce the Sumudu Neural Operator (SNO), a neural operator rooted in the properties of the Sumudu Transform. We leverage the relationship between the polynomial expansions of transform pairs to decompose the input space as…

Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface from its gradients. Traditional methods encounter significant challenges in achieving high accuracy and handling high-resolution inputs, particularly facing the…

Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within…

Background: It is still an open research area to theoretically understand why Deep Neural Networks (DNNs)---equipped with many more parameters than training data and trained by (stochastic) gradient-based methods---often achieve remarkably…

We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a…

We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…

This short note proposes a model-driven conditional Fourier neural operator (MD-CFNO) for synthetic turbulence generation. Spectrum-consistent synthetic turbulence is essential for inflow boundary construction in computational fluid…

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented…

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…

Neural fields have emerged as a new paradigm for representing signals, thanks to their ability to do it compactly while being easy to optimize. In most applications, however, neural fields are treated like black boxes, which precludes many…

Networks are widely used in many fields for their powerful ability to provide vivid representations of relationships between variables. However, many of them may be corrupted by experimental noise or inappropriate network inference methods…

Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required…

Artificial neural networks (ANNs) have now been widely used for industry applications and also played more important roles in fundamental researches. Although most ANN hardware systems are electronically based, optical implementation is…

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…

Graph Neural Networks (GNNs) have established themselves as the leading models for learning on graph-structured data, generally categorized into spatial and spectral approaches. Central to these architectures is the Graph Shift Operator…

Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to…

This study aims to develop surrogate models for accelerating decision making processes associated with carbon capture and storage (CCS) technologies. Selection of sub-surface $CO_2$ storage sites often necessitates expensive and involved…

Pansharpening aims to synthesize high-resolution multispectral (HR-MS) images by fusing the spatial textures of panchromatic (PAN) images with the spectral information of low-resolution multispectral (LR-MS) images. While recent deep…

Geological carbon sequestration (GCS) involves injecting CO$_2$ into subsurface geological formations for permanent storage. Numerical simulations could guide decisions in GCS projects by predicting CO$_2$ migration pathways and the…