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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.…

Machine Learning · Computer Science 2023-10-03 Wenhui Peng , Shaoxiang Qin , Senwen Yang , Jianchun Wang , Xue Liu , Liangzhu Leon Wang

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our…

Machine Learning · Computer Science 2024-02-19 Rixin Yu , Erdzan Hodzic

We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…

Machine Learning · Computer Science 2026-04-08 Zhexian Li , Ketan Savla

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

Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within…

Machine Learning · Computer Science 2026-05-05 Michael F. Staddon

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of…

Fluid Dynamics · Physics 2023-01-23 Peter I Renn , Cong Wang , Sahin Lale , Zongyi Li , Anima Anandkumar , Morteza Gharib

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…

Machine Learning · Computer Science 2025-10-21 Daniil D. Sirota , Sergey A. Khan , Sergey L. Kostikov , Kirill A. Butov

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…

Machine Learning · Statistics 2023-02-14 Navaneeth N , Tapas Tripura , Souvik Chakraborty

Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave…

Atmospheric and Oceanic Physics · Physics 2024-01-11 Svenja Ehlers , Marco Klein , Alexander Heinlein , Mathies Wedler , Nicolas Desmars , Norbert Hoffmann , Merten Stender

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent…

Machine Learning · Computer Science 2025-10-27 Qingsong Xu , Jonathan L Bamber , Nils Thuerey , Niklas Boers , Paul Bates , Gustau Camps-Valls , Yilei Shi , Xiao Xiang Zhu

The use of neural operators in a digital twin model of an offshore floating structure can provide a paradigm shift in structural response prediction and health monitoring, providing valuable information for real-time control. In this work,…

Atmospheric and Oceanic Physics · Physics 2023-12-04 Qianying Cao , Somdatta Goswami , Tapas Tripura , Souvik Chakraborty , George Em Karniadakis

Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier…

Fourier Neural Operators (FNO) have emerged as promising solutions for efficiently solving partial differential equations (PDEs) by learning infinite-dimensional function mappings through frequency domain transformations. However, the…

Machine Learning · Computer Science 2025-05-22 Tianyu Chen , Haoyi Zhou , Ying Li , Hao Wang , Zhenzhe Zhang , Tianchen Zhu , Shanghang Zhang , Jianxin Li

Simulation of urban wind environments is crucial for urban planning, pollution control, and renewable energy utilization. However, the computational requirements of high-fidelity computational fluid dynamics (CFD) methods make them…

Machine Learning · Computer Science 2025-01-13 Cheng Chen , Geng Tian , Shaoxiang Qin , Senwen Yang , Dingyang Geng , Dongxue Zhan , Jinqiu Yang , David Vidal , Liangzhu Leon Wang

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

Machine Learning · Computer Science 2026-03-11 Nanxi Chen , Airong Chen , Rujin Ma

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

Machine Learning · Computer Science 2021-08-16 Yu Huang , James Li , Min Shi , Hanqi Zhuang , Xingquan Zhu , Laurent Chérubin , James VanZwieten , Yufei Tang

With the recent rise of neural operators, scientific machine learning offers new solutions to quantify uncertainties associated with high-fidelity numerical simulations. Traditional neural networks, such as Convolutional Neural Networks…

Machine Learning · Computer Science 2024-09-04 Fanny Lehmann , Filippo Gatti , Michaël Bertin , Didier Clouteau

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Machine Learning · Computer Science 2023-02-03 Yesom Park , Jaemoo Choi , Changyeon Yoon , Chang hoon Song , Myungjoo Kang