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Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD).
A tensorial approach to computational continuum mechanics using object-oriented techniques
H. G. Weller, G. Tabor, H. Jasak, and C. Fureby · 1998
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A Quadrature Formula for the Sphere of the 131st Algebraic Order of Accuracy
V. Lebedev and D. Laikov · 1999
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An Introduction to Turbulent Flow
Jean Mathieu and Julian Scott · 2000
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Turbulent Flows
Stephen B. Pope · 2000
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On Layer Normalization in the Transformer Architecture
Ruibin Xiong, Yunchang Yang, Di He, Kai Zheng, Shuxin Zheng, Chen Xing, Huishuai Zhang, Yanyan Lan, Liwei Wang, and Tie-Yan Liu · 2002
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Is turbulence ergodic?
B. Galanti and A. Tsinober · 2004
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Denoising Diffusion Probabilistic Models
Jonathan Ho, Ajay Jain, and Pieter Abbeel · 2006
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Intermittency in Turbulence
J. Jiménez · 2006
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Matplotlib: A 2D graphics environment
J. D. Hunter · 2007
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A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence
Yi Li, Eric Perlman, Minping Wan, Yunke Yang, Charles Meneveau, Randal Burns, Shiyi Chen, Alexander Szalay, and Gregory Eyink · 2008
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SPHERE_LEBEDEV_RULE: Quadrature rules for the unit sphere, 2010
John Burkardt · 2010
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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 · 2010
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Turbulence in two dimensions
Nicholas T. Ouellette · 2012
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Time-resolved evolution of coherent structures in turbulent channels: Characterization of eddies and cascades
Adrián Lozano-Durán and Javier Jiménez · 2014
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Deep Residual Learning for Image Recognition, December 2015
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2015
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Acceleration of a Full-Scale Industrial CFD Application with OP2
István Z. Reguly, Gihan R. Mudalige, Carlo Bertolli, Michael B. Giles, Adam Betts, Paul H.J. Kelly, and David Radford · 2015
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U-Net: Convolutional Networks for Biomedical Image Segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 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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3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation
Özgün Çiçek, Ahmed Abdulkadir, Soeren S. Lienkamp, Thomas Brox, and Olaf Ronneberger · 2016
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Jupyter Notebooks - a publishing format for reproducible computational workflows
Thomas Kluyver, Benjamin Ragan-Kelley, Fernando Pérez, Brian Granger, Matthias Bussonnier, Jonathan Frederic, Kyle Kelley, Jessica Hamrick, Jason Grout, Sylvain Corlay, Paul Ivanov, Damián Avila, Safia Abdalla, Carol Willing, and Jupyter development team · 2016
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GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter · 2017
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Attention Is All You Need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin · 2017
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tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow
You Xie, Erik Franz, Mengyu Chu, and Nils Thuerey · 2017
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Enabling rootless Linux Containers in multi-user environments: The udocker tool
Jorge Gomes, Emanuele Bagnaschi, Isabel Campos, Mario David, Luís Alves, João Martins, João Pina, Alvaro López-García, and Pablo Orviz · 2018
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Fr\’echet ChemNet Distance: A metric for generative models for molecules in drug discovery, August 2018
Kristina Preuer, Philipp Renz, Thomas Unterthiner, Sepp Hochreiter, and Günter Klambauer · 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 · 2018
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3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, and Taco S Cohen · 2018
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Is vortex stretching the main cause of the turbulent energy cascade?
Maurizio Carbone and Andrew D. Bragg · 2019
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Deep Fluids: A Generative Network for Parameterized Fluid Simulations
Byungsoo Kim, Vinicius C. Azevedo, Nils Thuerey, Theodore Kim, Markus Gross, and Barbara Solenthaler · 2019
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DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation
Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove · 2019
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Learning Mesh-Based Simulation with Graph Networks
Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter W. Battaglia · 2021
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Universal Differential Equations for Scientific Machine Learning, November 2021
Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, and Alan Edelman · 2021
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E(n) Equivariant Graph Neural Networks
Víctor Garcia Satorras, Emiel Hoogeboom, and Max Welling · 2021
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Denoising Diffusion Implicit Models
Jiaming Song, Chenlin Meng, and Stefano Ermon · 2021
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AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions
Florent Bonnet, Ahmed Jocelyn Mazari, Paola Cinnella, and Patrick Gallinari · 2022
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PyTorch: An Imperative Style, High-Performance Deep Learning Library, December 2019
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 · 2019
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PyVista: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit (VTK)
Bane Sullivan and Alexander Kaszynski · 2019
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Towards Accurate Generative Models of Video: A New Metric & Challenges, March 2019
Thomas Unterthiner, Sjoerd van Steenkiste, Karol Kurach, Raphael Marinier, Marcin Michalski, and Sylvain Gelly · 2019
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Hydra - A framework for elegantly configuring complex applications
Omry Yadan · 2019
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Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
Marc Finzi, Samuel Stanton, Pavel Izmailov, and Andrew Gordon Wilson · 2020
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Array programming with NumPy
Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Haldane, Jaime Fernández del Río, Mark Wiebe, Pearu Peterson, Pierre Gérard-Marchant, Kevin Sheppard, Tyler Reddy, Warren Weckesser, Hameer Abbasi, Christoph Gohlke, and Travis E. Oliphant · 2020
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CFDNet: A deep learning-based accelerator for fluid simulations
Octavi Obiols-Sales, Abhinav Vishnu, Nicholas Malaya, and Aparna Chandramowlishwaran · 2020
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Message Passing Neural PDE Solvers
Johannes Brandstetter, Daniel E. Worrall, and Max Welling · 2022
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FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness
Tri Dao, Daniel Y. Fu, Stefano Ermon, Atri Rudra, and Christopher Ré · 2022
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Generative Modeling of Turbulence
Claudia Drygala, Benjamin Winhart, Francesca di Mare, and Hanno Gottschalk · 2022
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Towards Multi-spatiotemporal-scale Generalized PDE Modeling, September 2022
Jayesh K. Gupta and Johannes Brandstetter · 2022
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Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditions
Masanobu Horie and Naoto Mitsume · 2022
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Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks
Marten Lienen and Stephan Günnemann · 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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Einops: Clear and reliable tensor manipulations with einstein-like notation
Alex Rogozhnikov · 2022
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High-Resolution Image Synthesis with Latent Diffusion Models
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer · 2022
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Learned Coarse Models for Efficient Turbulence Simulation
Kimberly Stachenfeld, Drummond B. Fielding, Dmitrii Kochkov, Miles Cranmer, Tobias Pfaff, Jonathan Godwin, Can Cui, Shirley Ho, Peter Battaglia, and Alvaro Sanchez-Gonzalez · 2022
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PDEBench: An Extensive Benchmark for Scientific Machine Learning
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Learning to Solve PDE-constrained Inverse Problems with Graph Networks
Qingqing Zhao, David B. Lindell, and Gordon Wetzstein · 2022
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Generalization capabilities of conditional GAN for turbulent flow under changes of geometry, February 2023
Claudia Drygala, Francesca di Mare, and Hanno Gottschalk · 2023
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EAGLE: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers
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Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting
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Add and Thin: Diffusion for Temporal Point Processes
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A physics-informed diffusion model for high-fidelity flow field reconstruction
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Consistency Models, March 2023
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A Denoising Diffusion Model for Fluid Field Prediction, January 2023
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