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We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows.
Introduction to Fourier analysis on Euclidean spaces
Elias M Stein and Guido Weiss · 1971
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Turbulence statistics in fully developed channel flow at low Reynolds number
John Kim, Parviz Moin, and Robert Moser · 1987
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Active turbulence control for drag reduction in wall-bounded flows
Haecheon Choi, Parviz Moin, and John Kim · 1994
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Suppressing wall turbulence by means of a transverse traveling wave
Yiqing Du and George Em Karniadakis · 2000
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Digital signal processing: principles, algorithms, and applications, 4/e
John G Proakis · 2007
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Invariant recurrent solutions embedded in a turbulent two-dimensional kolmogorov flow
Gary J Chandler and Rich R Kerswell · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Variational inference with normalizing flows
Danilo Rezende and Shakir Mohamed · 2015
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Deep unsupervised learning using nonequilibrium thermodynamics
Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli · 2015
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Unstructured large-eddy simulations of supersonic jets
Guillaume A Bres, Frank E Ham, Joseph W Nichols, and Sanjiva K Lele · 2017
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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Multi-scale deep neural networks for solving high dimensional pdes
Wei Cai and Zhi-Qin John Xu · 2019
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Resolvent-analysis-based design of airfoil separation control
Chi-An Yeh and Kunihiko Taira · 2019
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On the spectral bias of neural networks
Nasim Rahaman, Aristide Baratin, Devansh Arpit, Felix Draxler, Min Lin, Fred Hamprecht, Yoshua Bengio, and Aaron Courville · 2019
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Towards understanding the spectral bias of deep learning
Yuan Cao, Zhiying Fang, Yue Wu, Ding-Xuan Zhou, and Quanquan Gu · 2019
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Generative modeling by estimating gradients of the data distribution
Yang Song and Stefano Ermon · 2019
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Fourier Neural Operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2020
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A phase shift deep neural network for high frequency approximation and wave problems
Wei Cai, Xiaoguang Li, and Lizuo Liu · 2020
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Fourier features let networks learn high frequency functions in low dimensional domains
Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng · 2020
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Denoising diffusion probabilistic models
Jonathan Ho, Ajay Jain, and Pieter Abbeel · 2020
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Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2020
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Denoising diffusion pytorch
Phil Wang · 2020
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Frequency bias in neural networks for input of non-uniform density
Ronen Basri, Meirav Galun, Amnon Geifman, David Jacobs, Yoni Kasten, and Shira Kritchman · 2020
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Physics-informed machine learning
George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang · 2021
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Variable-order fractional models for wall-bounded turbulent flows
Fangying Song and George Em Karniadakis · 2021
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis · 2021
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On the eigenvector bias of fourier feature networks: From regression to solving multi-scale pdes with physics-informed neural networks
Sifan Wang, Hanwen Wang, and Paris Perdikaris · 2021
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Nils Thuerey, Philipp Holl, Maximilian Mueller, Patrick Schnell, Felix Trost, and Kiwon Um · 2021
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Real-time inference and extrapolation via a Diffusion-inspired Temporal Transformer Operator (ditto)
Oded Ovadia, Vivek Oommen, Adar Kahana, Ahmad Peyvan, Eli Turkel, and George Em Karniadakis · 2023
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On the Spectral Bias of Neural Networks in the Neural Tangent Kernel Regime
Benjamin Bowman · 2023
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From pinns to pikans: Recent advances in physics-informed machine learning
Juan Diego Toscano, Vivek Oommen, Alan John Varghese, Zongren Zou, Nazanin Ahmadi Daryakenari, Chenxi Wu, and George Em Karniadakis · 2024
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Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression
Zhen Zhang, Zongren Zou, Ellen Kuhl, and George Em Karniadakis · 2024
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Nazanin Ahmadi Daryakenari, Mario De Florio, Khemraj Shukla, and George Em Karniadakis · 2024
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Zijie Li, Kazem Meidani, and Amir Barati Farimani · 2022
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Learning two-phase microstructure evolution using neural operators and autoencoder architectures
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Enrui Zhang, Adar Kahana, Eli Turkel, Rishikesh Ranade, Jay Pathak, and George Em Karniadakis · 2022
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Elucidating the design space of diffusion-based generative models
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Deep-learning-based super-resolution reconstruction of high-speed imaging in fluids
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Towards multi-spatiotemporal-scale generalized pde modeling
Jayesh K Gupta and Johannes Brandstetter · 2022
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Physics-informed neural network simulation of thermal cavity flow
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Graph neural network operators: a review
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