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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

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

We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit…

Machine Learning · Computer Science 2023-05-31 Qianying Cao , Somdatta Goswami , George Em Karniadakis

Deep neural network models have shown a great potential in accelerating the simulation of fluid dynamic systems. Once trained, these models can make inference within seconds, thus can be extremely efficient. However, they suffer from a…

Fluid Dynamics · Physics 2022-02-23 Wenhui Peng , Zelong Yuan , Jianchun Wang

This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…

Machine Learning · Computer Science 2025-07-25 Wonjae Lee , Taeyoung Kim , Hyungbin Park

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,…

Machine Learning · Computer Science 2023-10-13 Karn Tiwari , N M Anoop Krishnan , Prathosh A P

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

Machine Learning · Computer Science 2026-05-11 Vasilis Niarchos , Angelos Sirbu , Sokratis Trifinopoulos

Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In…

Computational Physics · Physics 2026-01-16 Jeongjin Park , Grant Bruer , Huseyin Tuna Erdinc , Abhinav Prakash Gahlot , Felix J. Herrmann

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

Simulating Darcy flows in porous media is fundamental to understand the future flow behavior of fluids in hydrocarbon and carbon storage reservoirs. Geological models of reservoirs are often associated with high uncertainly leading to many…

Fluid Dynamics · Physics 2024-07-16 Daniel Badawi , Eduardo Gildin

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…

Machine Learning · Computer Science 2024-06-06 Karn Tiwari , N M Anoop Krishnan , A P Prathosh

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

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

Computational Physics · Physics 2026-03-27 Q. C. Dong , Zi-Xuan Su , Qing Huo Liu , Wen Chen , Zhizhang , Chen

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…

Machine Learning · Computer Science 2025-06-03 Jin Song , Kenji Kawaguchi , Zhenya Yan

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…

Machine Learning · Computer Science 2024-05-03 Zongyi Li , Daniel Zhengyu Huang , Burigede Liu , Anima Anandkumar

This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow within porous media. The architecture is adjusted to manage…

Computational Engineering, Finance, and Science · Computer Science 2024-07-04 Xinliang Liu , Xia Yang , Chen-Song Zhang , Lian Zhang , Li Zhao

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

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

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…

Computer Vision and Pattern Recognition · Computer Science 2022-03-29 John Guibas , Morteza Mardani , Zongyi Li , Andrew Tao , Anima Anandkumar , Bryan Catanzaro

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