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Extended magnetohydrodynamics (XMHD) is a fluid plasma model generalizing ideal MHD by taking into account the impact of Hall drift effects and the influence of electron inertial effects. XMHD has a Hamiltonian structure which has received…

Analysis of PDEs · Mathematics 2024-06-26 Christophe Cheverry , Nicolas Besse

Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…

Machine Learning · Computer Science 2025-04-01 Christopher Bülte , Philipp Scholl , Gitta Kutyniok

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…

Machine Learning · Computer Science 2026-01-13 Marimuthu Kalimuthu , David Holzmüller , Mathias Niepert

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…

Machine Learning · Computer Science 2025-02-18 Somdatta Goswami , Dimitris G. Giovanis , Bowei Li , Seymour M. J. Spence , Michael D. Shields

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…

Machine Learning · Computer Science 2023-03-03 Alasdair Tran , Alexander Mathews , Lexing Xie , Cheng Soon Ong

Efficient and accurate time-domain simulation of electromagnetic fields in complex photonic devices is critical for designing broadband and ultrafast optical components, yet it is often limited by the high computational cost of conventional…

Optics · Physics 2026-02-05 Zaifan Wu , Yue You , Xian Zhou , Fan Zhang

Recent progress in AI has established neural operators as powerful tools that can predict the evolution of partial differential equations, such as the Navier-Stokes equations. Some complex problems rely on sophisticated algorithms to deal…

Machine Learning · Computer Science 2025-05-21 Paolo Guida , William L. Roberts

Accurate urban microclimate analysis with wind velocity and temperature is vital for energy-efficient urban planning, supporting carbon reduction, enhancing public health and comfort, and advancing the low-altitude economy. However,…

We propose an accelerated computational fluid dynamics framework based on a hybrid Fourier Neural Operator-Lattice Boltzmann Method (FNO-LBM) for steady and unsteady weakly compressible flows. FNO-based initialization significantly…

Fluid Dynamics · Physics 2026-05-01 Alexandra Junk , Josef M. Winter , Meike Tütken , Steffen Schmidt , Nikolaus A. Adams

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…

Numerical Analysis · Mathematics 2025-05-22 Zi-Hao Guo , Hou-Biao Li

Density functional theory (DFT) is a cornerstone of computational chemistry and materials science, but its computational cost limits its use in large-scale and high-throughput applications. While machine learning has accelerated energy…

Chemical Physics · Physics 2026-03-18 Yingdi Jin , Xinming Qin , Ruichen Liu , Jie Liu , Zhenyu Li , Jinlong Yang

Underground hydrogen storage (UHS) is a promising energy storage option for the current energy transition to a low-carbon economy. Fast modeling of hydrogen plume migration and pressure field evolution is crucial for UHS field management.…

Machine Learning · Computer Science 2026-02-26 Tao Wang , Hewei Tang

Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…

Fluid Dynamics · Physics 2026-03-10 Jinhong Wang , Matei C. Ignuta-Ciuncanu , Ricardo F. Martinez-Botas , Teng Cao

Magnetohydrodynamic simulations of core-collapse supernovae have become increasingly mature and important in recent years. Magnetic fields take center stage in scenarios for explaining hypernova explosions, but are now also considered in…

High Energy Astrophysical Phenomena · Physics 2024-03-29 Bernhard Müller

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…

Machine Learning · Computer Science 2025-07-08 Weidong Wu , Yong Zhang , Lili Hao , Yang Chen , Xiaoyan Sun , Dunwei Gong

Hemodynamic analysis is essential for predicting aneurysm rupture and guiding treatment. While magnetic resonance flow imaging enables time-resolved volumetric blood velocity measurements, its low spatiotemporal resolution and…

Computer Vision and Pattern Recognition · Computer Science 2025-07-21 Kyriakos Flouris , Moritz Halter , Yolanne Y. R. Lee , Samuel Castonguay , Luuk Jacobs , Pietro Dirix , Jonathan Nestmann , Sebastian Kozerke , Ender Konukoglu

We present our ongoing work aimed at accelerating a particle-resolved direct numerical simulation model designed to study aerosol-cloud-turbulence interactions. The dynamical model consists of two main components - a set of fluid dynamics…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…

Machine Learning · Computer Science 2026-03-31 Huanshuo Dong , Hao Wu , Hong Wang , Qin-Yi Zhang , Zhezheng Hao

Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neural operator…

Materials Science · Physics 2024-01-12 Siavash Jafarzadeh , Stewart Silling , Ning Liu , Zhongqiang Zhang , Yue Yu