Related papers: Component Fourier Neural Operator for Singularly P…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

This short note proposes a model-driven conditional Fourier neural operator (MD-CFNO) for synthetic turbulence generation. Spectrum-consistent synthetic turbulence is essential for inflow boundary construction in computational fluid…

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…

Thermal management in 3D ICs is increasingly challenging due to higher power densities. Traditional PDE-solving-based methods, while accurate, are too slow for iterative design. Machine learning approaches like FNO provide faster…

Neural operators approximate PDE solution maps, but they need not respect the symmetries of the governing equation. In out-of-distribution (OOD) regimes, a standard neural operator must often learn coordinate alignment and physical…

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…

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of…

Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability.…

Neural operator models for solving partial differential equations (PDEs) often rely on global mixing mechanisms-such as spectral convolutions or attention-which tend to oversmooth sharp local dynamics and introduce high computational cost.…

In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the…

The numerical approximation of the Boltzmann collision operator presents significant challenges arising from its high dimensionality, nonlinear structure, and nonlocal integral form. In this work, we propose a Fourier Neural Operator (FNO)…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…

Neural operators have emerged as powerful deep learning frameworks for approximating solution operators of parameterized partial differential equations (PDE). However, current methods predominantly rely on multilayer perceptrons (MLPs) for…

Solving partial differential equations remains a central challenge in scientific machine learning. Neural operators offer a promising route by learning mappings between function spaces and enabling resolution-independent inference, yet they…

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…

Self-training techniques have shown remarkable value across many deep learning models and tasks. However, such techniques remain largely unexplored when considered in the context of learning fast solvers for systems of partial differential…

Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…

Increased demands for high-performance materials have led to advanced composite materials with complex hierarchical designs. However, designing a tailored material microstructure with targeted properties and performance is extremely…

Simulation tools for photoacoustic wave propagation have played a key role in advancing photoacoustic imaging by providing quantitative and qualitative insights into parameters affecting image quality. Classical methods for numerically…