Related papers: Sensitivity-Constrained Fourier Neural Operators f…

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…

Fourier Neural Operators (FNOs) have been promoted as fast, mesh-invariant surrogates for partial-differential equation solvers, with seismic studies reporting orders-of-magnitude speedup over classical methods. We revisit those claims by…

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…

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…

A standard practice in developing image recognition models is to train a model on a specific image resolution and then deploy it. However, in real-world inference, models often encounter images different from the training sets in resolution…

Laplace Neural Operators (LNOs) have recently emerged as a promising approach in scientific machine learning due to the ability to learn nonlinear maps between functional spaces. However, this framework often requires substantial amounts of…

Supervised deep learning methods typically require large datasets and high-quality labels to achieve reliable predictions. However, their performance often degrades when trained on imperfect labels. To address this challenge, we propose a…

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…

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical…

This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our…

We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly…

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…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Neural operators have emerged as a powerful, discretization-invariant framework for solving partial differential equations (PDEs). Although established approaches like the Deep Operator Network (DeepONet) have successfully achieved…

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…

High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets'…

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators…

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…

Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those originating from partial differential equations. Such characteristics render them an effective approach for simulating the time evolution of quantum…