Related papers: A comprehensive and fair comparison of two neural …

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…

A Fourier neural operator (FNO) is one of the physics-inspired machine learning methods. In particular, it is a neural operator. In recent times, several types of neural operators have been developed, e.g., deep operator networks, Graph…

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…

Fourier Neural Operators (FNOs) have emerged as leading surrogates for solver operators for various functional problems, yet their stability, generalization and frequency behavior lack a principled explanation. We present a systematic…

Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…

Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we…

We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal…

Focused ultrasound (FUS) therapy is a promising tool for optimally targeted treatment of spinal cord injuries (SCI), offering submillimeter precision to enhance blood flow at injury sites while minimizing impact on surrounding tissues.…

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…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

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…

Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier…

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…

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…

Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering…

With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…

Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are universal, in the sense that they can approximate any…