Related papers: Fourier neural operator for learning solutions to …

We study learning weak solutions to nonlinear hyperbolic partial differential equations (H-PDE), which have been difficult to learn due to discontinuities in their solutions. We use a physics-informed variant of the Fourier Neural Operator…

Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving inverse problems. In this paper, we propose an invertible…

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…

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…

Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For…

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…

Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are…

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of…

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

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…

Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based…

This paper presents a novel neural operator learning framework for designing boundary control to mitigate stop-and-go congestion on freeways. The freeway traffic dynamics are described by second-order coupled hyperbolic partial differential…

We consider the problem of traffic density estimation with sparse measurements from stationary roadside sensors. Our approach uses Fourier neural operators to learn macroscopic traffic flow dynamics from high-fidelity data. During…

High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

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…

Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D…