Related papers: Neural Integral Operators for Inverse Problems: An…
Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…
Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…
Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined…
Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…
Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…
Neural Operators (NOs) are a powerful deep learning framework designed to learn the solution operator that arise from partial differential equations. This study investigates NOs ability to capture the stiff spatio-temporal dynamics of the…
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…
A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For…
Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…
Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…
We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…
Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While…
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…
We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous…
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…
Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…
Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. However, for geometric PDEs whose inputs and outputs transform…
The success of building a high-resolution velocity model using machine learning is hampered by generalization limitations that often limit the success of the approach on field data. This is especially true when relying on neural operators…
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…