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In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…

Machine Learning · Computer Science 2023-03-10 Bian Li , Hanchen Wang , Shihang Feng , Xiu Yang , Youzuo Lin

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

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,…

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

Seismic wave arrival time measurements form the basis for numerous downstream applications. State-of-the-art approaches for phase picking use deep neural networks to annotate seismograms at each station independently, yet human experts…

Geophysics · Physics 2023-12-01 Hongyu Sun , Zachary E. Ross , Weiqiang Zhu , Kamyar Azizzadenesheli

Seismic phase picking is fundamental for microseismic monitoring and subsurface imaging. Manual processing is impractical for real-time applications and large sensor arrays, motivating the use of deep learning-based pickers trained on…

Geophysics · Physics 2026-04-10 Ayrat Abdullin , Umair Bin Waheed , Leo Eisner , Naveed Iqbal

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…

Fluid Dynamics · Physics 2025-11-04 Marco Cayuela , Vincent Le Chenadec , Peter Schmid , Taraneh Sayadi

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

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

Machine Learning · Computer Science 2024-03-06 Robert Joseph George , Jiawei Zhao , Jean Kossaifi , Zongyi Li , Anima Anandkumar

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical…

Machine Learning · Statistics 2024-01-11 Hewei Tang , Qingkai Kong , Joseph P. Morris

Fourier Neural Operators (FNOs) have been promoted as fast, mesh-invariant surrogates for partial-differential equation solvers, with seismic studies reporting orders-of-magnitude speedup over classical methods. We revisit those claims by…

Geophysics · Physics 2025-08-18 Dimitri Voytan , Litan Li

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

Seismic traveltime is critical information conveyed by seismic waves, widely utilized in various geophysical applications. Conventionally, the simulation of seismic traveltime involves solving the eikonal equation. However, the efficiency…

Geophysics · Physics 2024-04-09 Chao Song , Tianshuo Zhao , Umair bin Waheed , Cai Liu , Tian You

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

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

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…

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,…

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…

Computational Engineering, Finance, and Science · Computer Science 2025-11-13 Rad Haghi , Bipin Gaikwad , Abani Patra

Flood inundation forecast provides critical information for emergency planning before and during flood events. Real time flood inundation forecast tools are still lacking. High-resolution hydrodynamic modeling has become more accessible in…

Fluid Dynamics · Physics 2023-08-01 Alexander Y. Sun , Zhi Li , Wonhyun Lee , Qixing Huang , Bridget R. Scanlon , Clint Dawson

Full-waveform inversion (FWI) is a widely used technique in seismic processing to produce high resolution Earth models that fully explain the recorded seismic data. FWI is a local optimisation problem which aims to minimise in a…

Geophysics · Physics 2019-11-22 Christopher Zerafa , Pauline Galea , Cristiana Sebu
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