Related papers: Principled Operator Learning in Ocean Dynamics: Th…

Multi-scale dynamic wake modeling and prediction are essential for the real-time control and optimization of floating offshore wind turbines (FOWTs). In this study, wakes of FOWTs under coupled surge and pitch motions across a range of…

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness. However, FNO is observed to be ineffective with large Fourier kernels that parameterize more frequencies. Current…

Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent…

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper,…

Magnetohydrodynamics (MHD) plays a pivotal role in describing the dynamics of plasma and conductive fluids, essential for understanding phenomena such as the structure and evolution of stars and galaxies, and in nuclear fusion for plasma…

We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable…

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…

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…

Data assimilation (DA) is crucial for enhancing solutions to partial differential equations (PDEs), such as those in numerical weather prediction, by optimizing initial conditions using observational data. Variational DA methods are widely…

The inclusion of high-fidelity simulations of SOL turbulence and transient MHD events such as ELMs in highly iterative applications remains computationally prohibitive, limiting their use in design and control workflows. Understanding these…

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…

This paper investigates the temporal evolution of high-speed compressible fluids in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into sequential format compatible with FNO…

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…

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 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…