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Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

Computational Physics · Physics 2022-03-23 Lu Lu , Xuhui Meng , Shengze Cai , Zhiping Mao , Somdatta Goswami , Zhongqiang Zhang , George Em Karniadakis

Quantitative monitoring of subsurface changes is essential for ensuring the safety of geological CO2 sequestration. Full-waveform monitoring (FWM) can resolve these changes at high spatial resolution, but conventional deterministic…

Geophysics · Physics 2025-12-16 Haipeng Li , Nanzhe Wang , Louis J. Durlofsky , Biondo L. Biondi

Geological Carbon Sequestration (GCS) has emerged as a promising strategy for mitigating global warming, yet its effectiveness heavily depends on accurately characterizing subsurface flow dynamics. The inherent geological uncertainty,…

Geophysics · Physics 2025-08-26 Zhao Feng , Xin-Yang Liu , Meet Hemant Parikh , Junyi Guo , Pan Du , Bicheng Yan , Jian-Xun Wang

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

This work presents a novel approach to neural architecture search (NAS) that aims to increase carbon efficiency for the model design process. The proposed framework CE-NAS addresses the key challenge of high carbon cost associated with NAS…

Machine Learning · Computer Science 2024-07-19 Yiyang Zhao , Yunzhuo Liu , Bo Jiang , Tian Guo

A plethora of next-generation all-optical devices based on exciton-polaritons have been proposed in latest years, including prototypes of transistors, switches, analogue quantum simulators and others. However, for such systems consisting of…

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…

Fluid Dynamics · Physics 2026-01-22 Hongyuan Lin , Shizhao Wang

Long-term predictions of nonlinear dynamics of three-dimensional (3D) turbulence are very challenging for machine learning approaches. In this paper, we propose an implicit U-Net enhanced Fourier neural operator (IU-FNO) for stable and…

Fluid Dynamics · Physics 2023-08-02 Zhijie Li , Wenhui Peng , Zelong Yuan , Jianchun Wang

A Fourier neural operator (FNO) is one of the physics-inspired machine learning methods. In particular, it is a neural operator. In recent times, several types of neural operators have been developed, e.g., deep operator networks, Graph…

Machine Learning · Computer Science 2022-09-27 Taeyoung Kim , Myungjoo Kang

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

The accurate calculation and uncertainty quantification of the characteristics of spent nuclear fuel (SNF) play a crucial role in ensuring the safety, efficiency, and sustainability of nuclear energy production, waste management, and…

Machine Learning · Computer Science 2023-08-17 Arnau Albà , Andreas Adelmann , Lucas Münster , Dimitri Rochman , Romana Boiger

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness. However, FNO is observed to be ineffective with large Fourier kernels that parameterize more frequencies. Current…

Machine Learning · Computer Science 2024-10-10 Shaoxiang Qin , Fuyuan Lyu , Wenhui Peng , Dingyang Geng , Ju Wang , Xing Tang , Sylvie Leroyer , Naiping Gao , Xue Liu , Liangzhu Leon Wang

Energy-efficient ventilation control plays a vital role in reducing building energy consumption while ensuring occupant health and comfort. While Computational Fluid Dynamics (CFD) simulations provide detailed and physically accurate…

Systems and Control · Electrical Eng. & Systems 2025-11-20 Yuexin Bian , Oliver Schmidt , Yuanyuan Shi

A major challenge in computed tomography is reconstructing objects from incomplete data. An increasingly popular solution for these problems is to incorporate deep learning models into reconstruction algorithms. This study introduces a…

Numerical Analysis · Mathematics 2024-02-20 Knut Salomonsson , Eric Oldgren , Emanuel Ström , Ozan Öktem

Accurate prediction of machining deformation in structural components is essential for ensuring dimensional precision and reliability. Such deformation often originates from residual stress fields, whose distribution and influence vary…

Machine Learning · Computer Science 2025-09-17 Changqing Liu , Kaining Dai , Zhiwei Zhao , Tianyi Wu , Yingguang Li

Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach. This has motivated the use of fully connected artificial…

Computational Engineering, Finance, and Science · Computer Science 2021-10-11 Opeoluwa Owoyele , Pinaki Pal

We introduce a new approach using computer vision to predict the land surface displacement from subsurface geometry images for Carbon Capture and Sequestration (CCS). CCS has been proved to be a key component for a carbon neutral society.…

Computer Vision and Pattern Recognition · Computer Science 2024-03-20 Wei Chen , Yunan Li , Yuan Tian

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…

In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Building on the structure of Fourier Neural Operators (FNO),…

Numerical Analysis · Mathematics 2025-04-28 Zilan Cheng , Zhongjian Wang , Li-Lian Wang , Mejdi Azaiez

FourNetFlows, the abbreviation of Fourier Neural Network for Airfoil Flows, is an efficient model that provides quick and accurate predictions of steady airfoil flows. We choose the Fourier Neural Operator (FNO) as the backbone architecture…

Fluid Dynamics · Physics 2022-07-12 Yuanjun Dai , Yiran An , Zhi Li