Related papers: Universal Fourier Neural Operators for periodic ho…

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…

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error…

Ultrasound-based elasticity imaging is a non-invasive technique for estimating tissue stiffness fields from displacement fields obtained by comparing ultrasound signals before and after compression. While recent deep learning approaches…

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…

High-fidelity simulations of laser welding capture complex thermo-fluid phenomena, including phase change, free-surface deformation, and keyhole dynamics, however their computational cost limits large-scale process exploration and real-time…

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…

Reliable digital twins of lithium-ion batteries must achieve high physical fidelity with sub-millisecond speed. In this work, we benchmark three operator-learning surrogates for the Single Particle Model (SPM): Deep Operator Networks…

With the recent rise of neural operators, scientific machine learning offers new solutions to quantify uncertainties associated with high-fidelity numerical simulations. Traditional neural networks, such as Convolutional Neural Networks…

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 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…

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 is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main model architectures used for operator learning. The FNO combines…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…

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…

In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we use the Fourier Neural Operator (FNO), a learning mapping…

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…

Efficient and accurate time-domain simulation of electromagnetic fields in complex photonic devices is critical for designing broadband and ultrafast optical components, yet it is often limited by the high computational cost of conventional…

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…