Related papers: A Resolution Independent Neural Operator
Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…
This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight…
In this paper, we propose a multiscale DeepONet to represent nonlinear operator between Banach spaces of highly oscillatory continuous functions. The multiscale deep neural network (DNN) utilizes a multiple scaling technique to convert high…
Deep neural networks have a good success record and are thus viewed as the best architecture choice for complex applications. Their main shortcoming has been, for a long time, the vanishing gradient which prevented the numerical…
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…
DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite dimensional Banach spaces. We analyze DeepONets and prove estimates on the resulting approximation and generalization errors. In…
By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…
In this work, we consider the non-invasive medical imaging modality of Electrical Impedance Tomography (EIT), where the goal is to recover the conductivity in a medium from boundary current-to-voltage measurements, i.e., the…
We propose a randomized neural network approach called RaNNDy for learning transfer operators and their spectral decompositions from data. The weights of the hidden layers of the neural network are randomly selected and only the output…
Deep neural networks (DNNs) are widely studied in various applications. A DNN consists of layers of neurons that compute affine combinations, apply nonlinear operations, and produce corresponding activations. The rectified linear unit…
Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…
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…
In this paper, we propose a deep neural network architecture for object recognition based on recurrent neural networks. The proposed network, called ReNet, replaces the ubiquitous convolution+pooling layer of the deep convolutional neural…
Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an…
Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to…
Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either…
A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…
Neural Operators (NOs) have emerged as powerful tools for learning mappings between function spaces. Among them, the kernel integral operator has been widely used in universally approximating architectures. Following the original…
This work proposes a Neural Network model that can control its depth using an iterate-to-fixed-point operator. The architecture starts with a standard layered Network but with added connections from current later to earlier layers, along…
Coarse-to-fine schemes are widely used in traditional single-image motion deblur; however, in the context of deep learning, existing multi-scale algorithms not only require the use of complex modules for feature fusion of low-scale RGB…