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We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models.
Statistical estimation of the parameters of a pde
Colin Fox and Geoff Nicholls · 2001
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The meshless finite element method
Sergio R Idelsohn, Eugenio Onate, Nestor Calvo, and Facundo Del Pin · 2003
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Partial differential equations and the finite element method
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Estimation of non-normalized statistical models by score matching
Aapo Hyvärinen and Peter Dayan · 2005
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Overview of pdes and their regulation
Kenji Omori and Jun Kotera · 2007
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Partial differential equations: An introduction
Walter A Strauss · 2007
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Numerical approximation of partial differential equations
Alfio Quarteroni and Alberto Valli · 2008
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Solution to pdes using radial basis function finite-differences (rbf-fd) on multiple gpus
Evan F Bollig, Natasha Flyer, and Gordon Erlebacher · 2012
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A penalty method for pde-constrained optimization in inverse problems
Tristan van Leeuwen and Felix J Herrmann · 2015
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Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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First-order and second-order adjoint methods for the inverse problem of identifying non-linear parameters in pdes
M Cho, B Jadamba, R Kahler, AA Khan, and M Sama · 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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Difftaichi: Differentiable programming for physical simulation
Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Frédo Durand · 2019
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Boundary element methods
Ferri MH Aliabadi · 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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Denoising diffusion probabilistic models
Jonathan Ho, Ajay Jain, and Pieter Abbeel · 2020
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Physics-informed neural networks for high-speed flows
Zhiping Mao, Ameya D Jagtap, and George Em Karniadakis · 2020
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Physics-informed neural networks for power systems
George S Misyris, Andreas Venzke, and Spyros Chatzivasileiadis · 2020
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Learning continuous-time pdes from sparse data with graph neural networks
Valerii Iakovlev, Markus Heinonen, and Harri Lähdesmäki · 2020
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Denoising diffusion implicit models
Jiaming Song, Chenlin Meng, and Stefano Ermon · 2020
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Physics-informed neural operator for learning partial differential equations
Zongyi Li, Hongkai Zheng, Nikola Kovachki, David Jin, Haoxuan Chen, Burigede Liu, Kamyar Azizzadenesheli, and Anima Anandkumar · 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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Physics-informed neural networks (pinns) for fluid mechanics: A review
Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, and George Em Karniadakis · 2021
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Physics-informed neural networks for heat transfer problems
Shengze Cai, Zhicheng Wang, Sifan Wang, Paris Perdikaris, and George Em Karniadakis · 2021
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Real-time neural radiance caching for path tracing
Thomas Müller, Fabrice Rousselle, Jan Novák, and Alexander Keller · 2021
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Transformer for partial differential equations’ operator learning
Zijie Li, Kazem Meidani, and Amir Barati Farimani · 2022
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State of the art on diffusion models for visual computing
Ryan Po, Wang Yifan, Vladislav Golyanik, Kfir Aberman, Jonathan T Barron, Amit H Bermano, Eric Ryan Chan, Tali Dekel, Aleksander Holynski, Angjoo Kanazawa, et al · 2023
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Diffusion models: A comprehensive survey of methods and applications
Ling Yang, Zhilong Zhang, Yang Song, Shenda Hong, Runsheng Xu, Yue Zhao, Wentao Zhang, Bin Cui, and Ming-Hsuan Yang · 2023
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Fourier neural operator surrogate model to predict 3d seismic waves propagation
Fanny Lehmann, Filippo Gatti, Michaël Bertin, and Didier Clouteau · 2023
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Solving seismic wave equations on variable velocity models with fourier neural operator
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An introduction to finite element methods for inverse coefficient problems in elliptic pdes
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Solving inverse-pde problems with physics-aware neural networks
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Diffusion models beat gans on image synthesis
Prafulla Dhariwal and Alexander Nichol · 2021
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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 · 2021
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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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Partial differential equations
Lawrence C Evans · 2022
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Physics-informed neural networks for solving reynolds-averaged navier–stokes equations
Hamidreza Eivazi, Mojtaba Tahani, Philipp Schlatter, and Ricardo Vinuesa · 2022
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Linear attention coupled fourier neural operator for simulation of three-dimensional turbulence
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Spherical fourier neural operators: Learning stable dynamics on the sphere
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Neural caches for monte carlo partial differential equation solvers
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Accelerating particle and fluid simulations with differentiable graph networks for solving forward and inverse problems
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Neural inverse operators for solving pde inverse problems
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Inversion-free image editing with natural language
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From zero to turbulence: Generative modeling for 3d flow simulation
Marten Lienen, David Lüdke, Jan Hansen-Palmus, and Stephan Günnemann · 2023
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A denoising diffusion model for fluid field prediction
Gefan Yang and Stefan Sommer · 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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Geometry-informed neural operator for large-scale 3d pdes
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