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The Fokker-Planck (FP) equation is a foundational PDE in stochastic processes.
Estimation of non-normalized statistical models by score matching
Aapo Hyvärinen and Peter Dayan · 2005
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Finite element method for the space and time fractional Fokker–Planck equation
Weihua Deng · 2009
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Stochastic differential equations: an introduction with applications
Bernt Oksendal · 2013
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Numerical solution of non-linear Fokker–Planck equation using finite differences method and the cubic spline functions
Behnam Sepehrian and Marzieh Karimi Radpoor · 2015
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JAX: composable transformations of Python+NumPy programs, 2018
James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang · 2018
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Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, and Weinan E · 2018
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Deep splitting method for parabolic PDEs
Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, and Ariel Neufeld · 2019
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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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Sliced score matching: A scalable approach to density and score estimation
Yang Song, Sahaj Garg, Jiaxin Shi, and Stefano Ermon · 2019
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Christian Beck, Lukas Gonon, and Arnulf Jentzen · 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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Normalizing flows: An introduction and review of current methods
Ivan Kobyzev, Simon JD Prince, and Marcus A Brubaker · 2020
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Efficient learning of generative models via finite-difference score matching
Tianyu Pang, Kun Xu, Chongxuan Li, Yang Song, Stefano Ermon, and Jun Zhu · 2020
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Solving inverse stochastic problems from discrete particle observations using the Fokker–Planck equation and physics-informed neural networks
Xiaoli Chen, Liu Yang, Jinqiao Duan, and George Em Karniadakis · 2021
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Solving time dependent Fokker-Planck equations via temporal normalizing flow
Xiaodong Feng, Li Zeng, and Tao Zhou · 2021
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Multilevel picard iterations for solving smooth semilinear parabolic heat equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, et al · 2021
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Adaptive deep density approximation for Fokker-Planck equations
Kejun Tang, Xiaoliang Wan, and Qifeng Liao · 2022
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High-dimensional gaussian sampling: A review and a unifying approach based on a stochastic proximal point algorithm
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Is $l^2$ physics informed loss always suitable for training physics informed neural network?
Chuwei Wang, Shanda Li, Di He, and Liwei Wang · 2022
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A deep learning method for solving Fokker-Planck equations
Jiayu Zhai, Matthew Dobson, and Yao Li · 2022
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Solving Fokker–Planck equations using deep kd-tree with a small amount of data
Hao Zhang, Yong Xu, Qi Liu, Xiaolong Wang, and Yongge Li · 2022
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Learning physics-informed neural networks without stacked back-propagation
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Density estimation using deep generative neural networks
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Physics-informed neural networks with hard constraints for inverse design
Lu Lu, Raphael Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, and Steven G Johnson · 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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Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models
Ling Guo, Hao Wu, and Tao Zhou · 2022
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Regularizing score-based models with score Fokker-Planck equations
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Learning the temporal evolution of multivariate densities via normalizing flows
Yubin Lu, Romit Maulik, Ting Gao, Felix Dietrich, Ioannis G Kevrekidis, and Jinqiao Duan · 2022
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Di He, Shanda Li, Wenlei Shi, Xiaotian Gao, Jia Zhang, Jiang Bian, Liwei Wang, and Tie-Yan Liu · 2023
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Hutchinson trace estimation for high-dimensional and high-order physics-informed neural networks
Zheyuan Hu, Zekun Shi, George Em Karniadakis, and Kenji Kawaguchi · 2023
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Tackling the curse of dimensionality with physics-informed neural networks
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Zheyuan Hu, Zhouhao Yang, Yezhen Wang, George Em Karniadakis, and Kenji Kawaguchi · 2023
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Michael Penwarden, Ameya D Jagtap, Shandian Zhe, George Em Karniadakis, and Robert M Kirby · 2023
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Tensor-compressed back-propagation-free training for (physics-informed) neural networks
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