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Physics-informed deep learning has been developed as a novel paradigm for learning physical dynamics recently.
An introduction to fluid dynamics
G. B. Whitham · 1969
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The finite element method
O. C. Zienkiewicz, R. L. Taylor, P. Nithiarasu, and J. Zhu · 1977
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Imaging of short ocean wind waves: a critical theoretical review
Bernd Jähne, Jochen Klinke, and Stefan Waas · 1994
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Finite volume methods
Robert Eymard, Thierry Gallouët, and Raphaèle Herbin · 2000
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On the efficient numerical simulation of directionally spread surface water waves
W.J.D. Bateman, C. Swan, and P.H. Taylor · 2001
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Estimation of non-normalized statistical models by score matching
Aapo Hyvärinen and Peter Dayan · 2005
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A connection between score matching and denoising autoencoders
Pascal Vincent · 2011
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A machine learning strategy to assist turbulence model development
Brendan D. Tracey, Karthik Duraisamy, and Juan J. Alonso · 2015
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New approaches in turbulence and transition modeling using data-driven techniques
Karthik Duraisamy, Ze Jia Zhang, and Anand Pratap Singh · 2015
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Deep learning in fluid dynamics
J. Nathan Kutz · 2017
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Dgm: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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Pde-net: Learning pdes from data
Zichao Long, Yiping Lu, Xin Ma, and Bin Dong · 2018
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G.E. Karniadakis · 2019
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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
Yinhao Zhu, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis, and Paris Perdikaris · 2019
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Generative modeling by estimating gradients of the data distribution
Yang Song and Stefano Ermon · 2019
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Physics-informed neural networks for cardiac activation mapping
Francisco Sahli Costabal, Yibo Yang, Paris Perdikaris, Daniel E. Hurtado, and Ellen Kuhl · 2020
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Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4d flow mri data using physics-informed neural networks
Georgios Kissas, Yibo Yang, Eileen Hwuang, Walter R. Witschey, John A. Detre, and Paris Perdikaris · 2020
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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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Multipole graph neural operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Andrew Stuart, Kaushik Bhattacharya, and Anima Anandkumar · 2020
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Teaching the incompressible navier–stokes equations to fast neural surrogate models in three dimensions
Nils Wandel, Michael Weinmann, and R. Klein · 2020
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Nils Wandel, Michael Weinmann, and R. Klein · 2020
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Towards physics-informed deep learning for turbulent flow prediction
Rui Wang, Karthik Kashinath, Mustafa Mustafa, Adrian Albert, and Rose Yu · 2020
Cited alongside, same era.
Modeling the dynamics of pde systems with physics-constrained deep auto-regressive networks
Nicholas Geneva and Nicholas Zabaras · 2020
Cited alongside, same era.
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Maziar Raissi, Alireza Yazdani, and George Em Karniadakis · 2020
Cited alongside, same era.
Denoising diffusion probabilistic models
Jonathan Ho, Ajay Jain, and Pieter Abbeel · 2020
Cited alongside, same era.
Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2020
Cited alongside, same era.
Physics-informed pointnet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries
Ali Kashefi and Tapan Mukerji · 2022
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Come-closer-diffuse-faster: Accelerating conditional diffusion models for inverse problems through stochastic contraction
Hyungjin Chung, Byeongsu Sim, and Jong Chul Ye · 2022
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Repaint: Inpainting using denoising diffusion probabilistic models
Andreas Lugmayr, Martin Danelljan, Andres Romero, Fisher Yu, Radu Timofte, and Luc Van Gool · 2022
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Progressive deblurring of diffusion models for coarse-to-fine image synthesis
Sangyun Lee, Hyungjin Chung, Jaehyeon Kim, and Jong Chul Ye · 2022
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Image super-resolution via iterative refinement
Chitwan Saharia, Jonathan Ho, William Chan, Tim Salimans, David J Fleet, and Mohammad Norouzi · 2022
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Improved techniques for training score-based generative models
Yang Song and Stefano Ermon · 2020
Cited alongside, same era.
Denoising diffusion implicit models
Jiaming Song, Chenlin Meng, and Stefano Ermon · 2020
Cited alongside, same era.
Uncovering near-wall blood flow from sparse data with physics-informed neural networks
Amirhossein Arzani, Jian-Xun Wang, and Roshan M. D’Souza · 2021
Cited alongside, same era.
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
Cited alongside, same era.
Diffusion models beat gans on image synthesis
Prafulla Dhariwal and Alexander Nichol · 2021
Cited alongside, same era.
Neural operator: Learning maps between function spaces
Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2021
Cited alongside, same era.
Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations
Xiaowei Jin, Shengze Cai, Hui Li, and George Em Karniadakis · 2021
Cited alongside, same era.
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Deblurring via stochastic refinement
Jay Whang, Mauricio Delbracio, Hossein Talebi, Chitwan Saharia, Alexandros G Dimakis, and Peyman Milanfar · 2022
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Pretraining is all you need for image-to-image translation
Tengfei Wang, Ting Zhang, Bo Zhang, Hao Ouyang, Dong Chen, Qifeng Chen, and Fang Wen · 2022
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Palette: Image-to-image diffusion models
Chitwan Saharia, William Chan, Huiwen Chang, Chris Lee, Jonathan Ho, Tim Salimans, David Fleet, and Mohammad Norouzi · 2022
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Diffusion posterior sampling for general noisy inverse problems
Hyungjin Chung, Jeongsol Kim, Michael T Mccann, Marc L Klasky, and Jong Chul Ye · 2022
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Improving diffusion models for inverse problems using manifold constraints
Hyungjin Chung, Byeongsu Sim, Dohoon Ryu, and Jong Chul Ye · 2022
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Parallel diffusion models of operator and image for blind inverse problems
Hyungjin Chung, Jeongsol Kim, Sehui Kim, and Jong Chul Ye · 2022
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Zero-shot image restoration using denoising diffusion null-space model
Yinhuai Wang, Jiwen Yu, and Jian Zhang · 2022
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Nithin Gopalakrishnan Nair, Kangfu Mei, and Vishal M Patel · 2022
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Pdebench: An extensive benchmark for scientific machine learning
Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Dan MacKinlay, Francesco Alesiani, Dirk Pflüger, and Mathias Niepert · 2022
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Numerical calculation of the portal pressure gradient of the human liver with a domain decomposition method
Z. Lin, B. Wu, S. Qin, X. Wang, R. Chen, and XC Cai · 2022
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Tdstf: Transformer-based diffusion probabilistic model for sparse time series forecasting
Ping Chang, Huayu Li, Stuart F Quan, Janet Roveda, and Ao Li · 2023
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Ambiguous medical image segmentation using diffusion models
Aimon Rahman, Jeya Maria Jose Valanarasu, Ilker Hacihaliloglu, and Vishal M Patel · 2023
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Diffusion models for memory-efficient processing of 3d medical images
Florentin Bieder, Julia Wolleb, Alicia Durrer, Robin Sandkühler, and Philippe C Cattin · 2023
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Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence
Arvind T. Mohan, Nicholas Lubbers, Misha Chertkov, and Daniel Livescu · 2023
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A physics-informed diffusion model for high-fidelity flow field reconstruction
Dule Shu, Zijie Li, and Amir Barati Farimani · 2023
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