Related papers: Multi-Resolution Active Learning of Fourier Neural…
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…
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…
Modeling high-frequency information is a critical challenge in scientific machine learning. For instance, fully turbulent flow simulations of the Navier-Stokes equations at Reynolds numbers 3500 and above can generate high-frequency signals…
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…
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…
Neural operators, such as Fourier Neural Operators (FNO), form a principled approach for learning solution operators for PDEs and other mappings between function spaces. However, many real-world problems require high-resolution training…
Microstructural evolution, particularly grain growth, plays a critical role in shaping the physical, optical, and electronic properties of materials. Traditional phase-field modeling accurately simulates these phenomena but is…
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 (FNOs) have emerged as promising surrogates for partial differential equation solvers. In this work, we extensively tested FNOs on a variety of systems with non-linear and non-stationary properties, using a wide…
Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…
Neural operators have emerged as a powerful, data-driven paradigm for learning solution operators of partial differential equations (PDEs). State-of-the-art architectures, such as the Fourier Neural Operator (FNO), have achieved remarkable…
Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…
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…
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…
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…
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…
Exploring the outer atmosphere of the sun has remained a significant bottleneck in astrophysics, given the intricate magnetic formations that significantly influence diverse solar events. Magnetohydrodynamics (MHD) simulations allow us to…
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…
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…
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…