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Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance.
“PyTorch: An Imperative Style, High-Performance Deep Learning Library”
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Köpf, Edward Yang, Zach DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai and Soumith Chintala · 1912
Earlier work this paper cites.
“PyTorch: An Imperative Style, High-Performance Deep Learning Library”
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Köpf, Edward Yang, Zach DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai and Soumith Chintala · 1912
Earlier work this paper cites.
“Notes on the History of Correlation”
Karl Pearson · 1920
Earlier work this paper cites.
“Notes on the History of Correlation”
Karl Pearson · 1920
Earlier work this paper cites.
“A Review of the Statistical Theory of Turbulence”
Hugh. Dryden · 1943
Earlier work this paper cites.
“A Review of the Statistical Theory of Turbulence”
Hugh. Dryden · 1943
Earlier work this paper cites.
“Atmospheric Turbulence”
John. Wyngaard · 1992
Earlier work this paper cites.
“Atmospheric Turbulence”
John. Wyngaard · 1992
Earlier work this paper cites.
“Direct Numerical Simulation: A Tool in Turbulence Research”
Parviz Moin and Krishnan Mahesh · 1998
Earlier work this paper cites.
“Direct Numerical Simulation: A Tool in Turbulence Research”
Parviz Moin and Krishnan Mahesh · 1998
Earlier work this paper cites.
“Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions”
Mette Olufsen, Charles Peskin, Won Kim, Erik Pedersen, Ali Nadim and Jesper Larsen · 2000
Earlier work this paper cites.
“Turbulent Flows”
Stephen Pope · 2000
Earlier work this paper cites.
“Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions”
Mette Olufsen, Charles Peskin, Won Kim, Erik Pedersen, Ali Nadim and Jesper Larsen · 2000
Earlier work this paper cites.
“Turbulent Flows”
Stephen Pope · 2000
Earlier work this paper cites.
“Estimation of Non-Normalized Statistical Models by Score Matching”
Aapo Hyvärinen · 2005
Earlier work this paper cites.
“Estimation of Non-Normalized Statistical Models by Score Matching”
Aapo Hyvärinen · 2005
Earlier work this paper cites.
“A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities”
Philippe Spalart, Sebastien Deck, Michael. Shur, Kyle Squires, Michael Strelets and Andrey Travin · 2006
Earlier work this paper cites.
“A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities”
Philippe Spalart, Sebastien Deck, Michael. Shur, Kyle Squires, Michael Strelets and Andrey Travin · 2006
Earlier work this paper cites.
“Data Exploration of Turbulence Simulations Using a Database Cluster”
Eric Perlman, Randal Burns, Yi Li and Charles Meneveau · 2007
Earlier work this paper cites.
“Data Exploration of Turbulence Simulations Using a Database Cluster”
Eric Perlman, Randal Burns, Yi Li and Charles Meneveau · 2007
Earlier work this paper cites.
“Auto-Encoding Variational Bayes”
Diederik. Kingma and Max Welling · 2014
Earlier work this paper cites.
“Auto-Encoding Variational Bayes”
Diederik. Kingma and Max Welling · 2014
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“SU2: An Open-Source Suite for Multiphysics Simulation and Design”
Thomas Economon, Francisco Palacios, Sean Copeland, Trent Lukaczyk and Juan Alonso · 2015
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“Adam: A Method for Stochastic Optimization”
Diederik. Kingma and Jimmy Ba · 2015
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“U-Net: Convolutional Networks for Biomedical Image Segmentation”
Olaf Ronneberger, Philipp Fischer and Thomas Brox · 2015
Earlier work this paper cites.
“Deep Unsupervised Learning Using Nonequilibrium Thermodynamics”
Jascha Sohl-Dickstein, Eric. Weiss, Niru Maheswaranathan and Surya Ganguli · 2015
Earlier work this paper cites.
“SU2: An Open-Source Suite for Multiphysics Simulation and Design”
Thomas Economon, Francisco Palacios, Sean Copeland, Trent Lukaczyk and Juan Alonso · 2015
Earlier work this paper cites.
“Adam: A Method for Stochastic Optimization”
Diederik. Kingma and Jimmy Ba · 2015
Earlier work this paper cites.
“U-Net: Convolutional Networks for Biomedical Image Segmentation”
Olaf Ronneberger, Philipp Fischer and Thomas Brox · 2015
Earlier work this paper cites.
“Deep Unsupervised Learning Using Nonequilibrium Thermodynamics”
Jascha Sohl-Dickstein, Eric. Weiss, Niru Maheswaranathan and Surya Ganguli · 2015
Earlier work this paper cites.
“Generating Images with Perceptual Similarity Metrics Based on Deep Networks”
Alexey Dosovitskiy and Thomas Brox · 2016
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“Deep Learning”
Ian Goodfellow, Yoshua Bengio and Aaron Courville · 2016
Earlier work this paper cites.
“Deep Residual Learning for Image Recognition”
Kaiming He, Xiangyu Zhang, Shaoqing Ren and Jian Sun · 2016
Earlier work this paper cites.
“Perceptual Losses for Real-Time Style Transfer and Super-Resolution”
Justin Johnson, Alexandre Alahi and Li Fei-Fei · 2016
Earlier work this paper cites.
“Generating Images with Perceptual Similarity Metrics Based on Deep Networks”
Alexey Dosovitskiy and Thomas Brox · 2016
Earlier work this paper cites.
“Deep Learning”
Ian Goodfellow, Yoshua Bengio and Aaron Courville · 2016
Earlier work this paper cites.
“Deep Residual Learning for Image Recognition”
Kaiming He, Xiangyu Zhang, Shaoqing Ren and Jian Sun · 2016
Earlier work this paper cites.
“Perceptual Losses for Real-Time Style Transfer and Super-Resolution”
Justin Johnson, Alexandre Alahi and Li Fei-Fei · 2016
Earlier work this paper cites.
“Unrolled Generative Adversarial Networks”
Luke Metz, Ben Poole, David Pfau and Jascha Sohl-Dickstein · 2017
Earlier work this paper cites.
“Attention Is All You Need”
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan. Gomez, Lukasz Kaiser and Illia Polosukhin · 2017
Earlier work this paper cites.
“Unrolled Generative Adversarial Networks”
Luke Metz, Ben Poole, David Pfau and Jascha Sohl-Dickstein · 2017
Earlier work this paper cites.
“Attention Is All You Need”
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan. Gomez, Lukasz Kaiser and Illia Polosukhin · 2017
Earlier work this paper cites.
“Deep Learning for Universal Linear Embeddings of Nonlinear Dynamics”
Bethany Lusch, J. Kutz and Steven. Brunton · 2018
Earlier work this paper cites.
“Efficient Collective Swimming by Harnessing Vortices through Deep Reinforcement Learning”
Siddhartha Verma, Guido Novati and Petros Koumoutsakos · 2018
Earlier work this paper cites.
“Group Normalization”
Yuxin Wu and Kaiming He · 2018
Earlier work this paper cites.
“Deep Learning for Universal Linear Embeddings of Nonlinear Dynamics”
Bethany Lusch, J. Kutz and Steven. Brunton · 2018
Earlier work this paper cites.
“Efficient Collective Swimming by Harnessing Vortices through Deep Reinforcement Learning”
Siddhartha Verma, Guido Novati and Petros Koumoutsakos · 2018
Earlier work this paper cites.
“Group Normalization”
Yuxin Wu and Kaiming He · 2018
Earlier work this paper cites.
“Learning Data Driven Discretizations for Partial Differential Equations”
Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey and Michael. Brenner · 2019
Earlier work this paper cites.
“Quantifying Model Form Uncertainty in Reynolds-Averaged Turbulence Models with Bayesian Deep Neural Networks”
Nicholas Geneva and Nicholas Zabaras · 2019
Earlier work this paper cites.
“Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks”
Nicholas Geneva and Nicholas Zabaras · 2019
Earlier work this paper cites.
“Deep Fluids: A Generative Network for Parameterized Fluid Simulations”
Byungsoo Kim, Vinicius. Azevedo, Nils Thuerey, Theodore Kim, Markus. Gross and Barbara Solenthaler · 2019
Earlier work this paper cites.
“Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow”
Steffen Wiewel, Moritz Becher and Nils Thuerey · 2019
Earlier work this paper cites.
“Learning Data Driven Discretizations for Partial Differential Equations”
Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey and Michael. Brenner · 2019
Earlier work this paper cites.
“Quantifying Model Form Uncertainty in Reynolds-Averaged Turbulence Models with Bayesian Deep Neural Networks”
Nicholas Geneva and Nicholas Zabaras · 2019
Earlier work this paper cites.
“Deep Fluids: A Generative Network for Parameterized Fluid Simulations”
Byungsoo Kim, Vinicius. Azevedo, Nils Thuerey, Theodore Kim, Markus. Gross and Barbara Solenthaler · 2019
Earlier work this paper cites.
“Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow”
Steffen Wiewel, Moritz Becher and Nils Thuerey · 2019
Cited alongside, same era.
“Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks”
Nicholas Geneva and Nicholas Zabaras · 2019
Cited alongside, same era.
“Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction”
Filipe avila-peresde-Peres, Thomas. Economon and J. Kolter · 2020
Cited alongside, same era.
“Denoising Diffusion Probabilistic Models”
Jonathan Ho, Ajay Jain and Pieter Abbeel · 2020
Cited alongside, same era.
“Learning to Control PDEs with Differentiable Physics”
Philipp Holl, Nils Thuerey and Vladlen Koltun · 2020
Cited alongside, same era.
“On the Risks of Using Double Precision in Numerical Simulations of Spatio-Temporal Chaos”
“Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding”
Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily. Denton, Seyed Ghasemipour, Raphael Lopes, Burcu Ayan, Tim Salimans, Jonathan Ho, David. Fleet and Mohammad Norouzi · 2022
Later among the works it cites.
“Progressive Distillation for Fast Sampling of Diffusion Models”
Tim Salimans and Jonathan Ho · 2022
Later among the works it cites.
“Solving Inverse Problems in Medical Imaging with Score-Based Generative Models”
Yang Song, Liyue Shen, Lei Xing and Stefano Ermon · 2022
Later among the works it cites.
“Learned Coarse Models for Efficient Turbulence Simulation”
Kimberly. Stachenfeld, Drummond Fielding, Dmitrii Kochkov, Miles. Cranmer, Tobias Pfaff, Jonathan Godwin, Can Cui, Shirley Ho, Peter. Battaglia and Alvaro Sanchez-Gonzalez · 2022
Later among the works it cites.
“PDEBench: An Extensive Benchmark for Scientific Machine Learning”
Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Daniel MacKinlay, Francesco Alesiani, Dirk Pflüger and Mathias Niepert · 2022
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Tianli Hu and Shijun Liao · 2020
Cited alongside, same era.
“Learning Similarity Metrics for Numerical Simulations”
Georg Kohl, Kiwon Um and Nils Thuerey · 2020
Cited alongside, same era.
“Learning to Simulate Complex Physics with Graph Networks”
Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec and Peter. Battaglia · 2020
Cited alongside, same era.
“DPM: A Deep Learning PDE Augmentation Method with Application to Large-Eddy Simulation”
Justin. Sirignano, Jonathan. MacArt and Jonathan. Freund · 2020
Cited alongside, same era.
“Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows”
Nils Thuerey, Konstantin Weissenow, Lukas Prantl and Xiangyu Hu · 2020
Cited alongside, same era.
“Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers”
Kiwon Um, Robert Brand, Yun Fei, Philipp Holl and Nils Thuerey · 2020
Cited alongside, same era.
“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.
“Physics-Based Deep Learning”
Nils Thuerey, Philipp Holl, Maximilian Mueller, Patrick Schnell, Felix Trost and Kiwon Um · 2022
Later among the works it cites.
“Learning to Accelerate Partial Differential Equations via Latent Global Evolution”
Tailin Wu, Takashi Maruyama and Jure Leskovec · 2022
Later among the works it cites.
“Message Passing Neural PDE Solvers”
Johannes Brandstetter, Daniel. Worrall and Max Welling · 2022
Later among the works it cites.
“Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction”
Hyungjin Chung, Byeongsu Sim and Jong Ye · 2022
Later among the works it cites.
“Flexible Diffusion Modeling of Long Videos”
William Harvey, Saeid Naderiparizi, Vaden Masrani, Christian Weilbach and Frank Wood · 2022
Later among the works it cites.
“Video Diffusion Models”
Jonathan Ho, Tim Salimans, Alexey. Gritsenko, William Chan, Mohammad Norouzi and David. Fleet · 2022
Later among the works it cites.
“Diffusion Models for Video Prediction and Infilling”
Tobias Höppe, Arash Mehrjou, Stefan Bauer, Didrik Nielsen and Andrea Dittadi · 2022
Later among the works it cites.
“Elucidating the Design Space of Diffusion-Based Generative Models”
Tero Karras, Miika Aittala, Timo Aila and Samuli Laine · 2022
Later among the works it cites.
“Denoising Diffusion Restoration Models”
Bahjat Kawar, Michael Elad, Stefano Ermon and Jiaming Song · 2022
Later among the works it cites.
“Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-Based Loss Functions and Optimisation Horizons”
Björn List, Li-Wei Chen and Nils Thuerey · 2022
Later among the works it cites.
“A ConvNet for the 2020s”
Zhuang Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell and Saining Xie · 2022
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“Diffusion Autoencoders: Toward a Meaningful and Decodable Representation”
Konpat Preechakul, Nattanat Chatthee, Suttisak Wizadwongsa and Supasorn Suwajanakorn · 2022
Later among the works it cites.
“Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding”
Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily. Denton, Seyed Ghasemipour, Raphael Lopes, Burcu Ayan, Tim Salimans, Jonathan Ho, David. Fleet and Mohammad Norouzi · 2022
Later among the works it cites.
“Progressive Distillation for Fast Sampling of Diffusion Models”
Tim Salimans and Jonathan Ho · 2022
Later among the works it cites.
“Solving Inverse Problems in Medical Imaging with Score-Based Generative Models”
Yang Song, Liyue Shen, Lei Xing and Stefano Ermon · 2022
Later among the works it cites.
“Learned Coarse Models for Efficient Turbulence Simulation”
Kimberly. Stachenfeld, Drummond Fielding, Dmitrii Kochkov, Miles. Cranmer, Tobias Pfaff, Jonathan Godwin, Can Cui, Shirley Ho, Peter. Battaglia and Alvaro Sanchez-Gonzalez · 2022
Later among the works it cites.
“PDEBench: An Extensive Benchmark for Scientific Machine Learning”
Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Daniel MacKinlay, Francesco Alesiani, Dirk Pflüger and Mathias Niepert · 2022
Later among the works it cites.
“Physics-Based Deep Learning”
Nils Thuerey, Philipp Holl, Maximilian Mueller, Patrick Schnell, Felix Trost and Kiwon Um · 2022
Later among the works it cites.
“Learning to Accelerate Partial Differential Equations via Latent Global Evolution”
Tailin Wu, Takashi Maruyama and Jure Leskovec · 2022
Later among the works it cites.
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