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The Fokker-Planck equation (FPE) is the partial differential equation that governs the density evolution of the It\^o process and is of great importance to the literature of statistical physics and machine learning.
A deterministic approximation of diffusion equations using particles
Pierre Degond and Francisco-José Mustieles · 1990
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The variational formulation of the fokker–planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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On the trend to equilibrium for the fokker-planck equation: an interplay between physics and functional analysis
Peter A Markowich and Cédric Villani · 2000
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Gradient flows: in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2005
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Optimal transport: old and new , volume 338
Cédric Villani · 2009
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Mean field games models—a brief survey
Diogo A Gomes et al · 2014
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A finite-volume method for nonlinear nonlocal equations with a gradient flow structure
José A Carrillo, Alina Chertock, and Yanghong Huang · 2015
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Fokker-planck equation and thermodynamic system analysis
Umberto Lucia and Gianpiero Gervino · 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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Learning population-level diffusions with generative rnns
Tatsunori Hashimoto, David Gifford, and Tommi Jaakkola · 2016
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Mean field limit and propagation of chaos for vlasov systems with bounded forces
Pierre-Emmanuel Jabin and Zhenfu Wang · 2016
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Low-dimensional reduced-order models for statistical response and uncertainty quantification: Two-layer baroclinic turbulence
Di Qi and Andrew J Majda · 2016
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
Arnak S Dalalyan · 2017
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Rafael Bailo, Jose A Carrillo, and Jingwei Hu · 2018
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Langevin monte carlo and jko splitting
Espen Bernton · 2018
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Neural ordinary differential equations
Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
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On the global convergence of gradient descent for over-parameterized models using optimal transport
Lenaic Chizat and Francis Bach · 2018
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Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, and E Weinan · 2018
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Pde-net: Learning pdes from data
An introduction to mean field game theory
Pierre Cardaliaguet and Alessio Porretta · 2020
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Ode to an ode
Krzysztof M Choromanski, Jared Quincy Davis, Valerii Likhosherstov, Xingyou Song, Jean-Jacques Slotine, Jacob Varley, Honglak Lee, Adrian Weller, and Vikas Sindhwani · 2020
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Neural parametric fokker-planck equations
Shu Liu, Wuchen Li, Hongyuan Zha, and Haomin Zhou · 2020
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Mean field analysis of neural networks: A central limit theorem
Justin Sirignano and Konstantinos Spiliopoulos · 2020
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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 · 2020
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Three ways to solve partial differential equations with neural networks—a review
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Zichao Long, Yiping Lu, Xianzhong Ma, and Bin Dong · 2018
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Augmented neural odes
Emilien Dupont, Arnaud Doucet, and Yee Whye Teh · 2019
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Stochastic runge-kutta accelerates langevin monte carlo and beyond
Xuechen Li, Yi Wu, Lester Mackey, and Murat A Erdogdu · 2019
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Understanding mcmc dynamics as flows on the wasserstein space
Chang Liu, Jingwei Zhuo, and Jun Zhu · 2019
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Pde-net 2.0: Learning pdes from data with a numeric-symbolic hybrid deep network
Zichao Long, Yiping Lu, and Bin Dong · 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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Transport analysis of infinitely deep neural network
Sho Sonoda and Noboru Murata · 2019
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Jan Blechschmidt and Oliver G Ernst · 2021
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Primal dual methods for wasserstein gradient flows
Jose A Carrillo, Katy Craig, Li Wang, and Chaozhen Wei · 2021
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Differential privacy dynamics of langevin diffusion and noisy gradient descent
Rishav Chourasia, Jiayuan Ye, and Reza Shokri · 2021
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Modeling from features: a mean-field framework for over-parameterized deep neural networks
Cong Fang, Jason Lee, Pengkun Yang, and Tong Zhang · 2021
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Sqrt (d) dimension dependence of langevin monte carlo
Ruilin Li, Hongyuan Zha, and Molei Tao · 2021
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Large-scale wasserstein gradient flows
Petr Mokrov, Alexander Korotin, Lingxiao Li, Aude Genevay, Justin M Solomon, and Evgeny Burnaev · 2021
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Scalable inference in sdes by direct matching of the fokker–planck–kolmogorov equation
Arno Solin, Ella Tamir, and Prakhar Verma · 2021
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