相关论文: Neural Operators Learn the Local Physics of Magnet…
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…
Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…
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…
Recent research in machine learning has employed neural networks to learn mappings between function spaces on bounded domains termed ``neural operators''. As such, these operators can provide alternatives to standard numerical methods for…
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…
Magnetohydrodynamics (MHD) couples the Navier--Stokes and Maxwell equations into a nonlinear system of partial differential equations governing stellar interiors, astrophysical jets, fusion plasmas, and space weather. Numerical advances,…
Magnetised plasma turbulence pervades the universe and is likely to play an important role in a variety of astrophysical settings. Magnetohydrodynamics (MHD) provides the simplest theoretical framework in which phenomenological models for…
This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…
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…
The modeling of multi-scale and multi-physics complex systems typically involves the use of scientific software that can optimally leverage extreme scale computing. Despite major developments in recent years, these simulations continue to…
A new neutrino magnetohydrodynamics (NMHD) model is formulated, where the effects of the charged weak current on the electron-ion magnetohydrodynamic fluid are taken into account. The model incorporates in a systematic way the role of the…
Modeling and simulation of High Power Microwave (HPM) breakdown, a multiscale phenomenon, is computationally expensive and requires solving Maxwell's equations (EM solver) coupled with a plasma continuity equation (plasma solver). In this…
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…
This paper explores Neural Operators to predict turbulent flows, focusing on the Fourier Neural Operator (FNO) model. It aims to develop reduced-order/surrogate models for turbulent flow simulations using Machine Learning. Different model…
Predicting plasma evolution within a Tokamak is crucial to building a sustainable fusion reactor. Whether in the simulation space or within the experimental domain, the capability to forecast the spatio-temporal evolution of plasma field…
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…
Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…
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…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
Global urbanization has underscored the significance of urban microclimates for human comfort, health, and building/urban energy efficiency. They profoundly influence building design and urban planning as major environmental impacts.…