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The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants, hence requiring the development of a data-driven modeling approach.
Variational inference for diffusion processes
Cédric Archambeau, Manfred Opper, Yuan Shen, Dan Cornford, and John S Shawe-Taylor · 2008
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A novel high order space-time spectral method for the time fractional Fokker-Planck equation
Minling Zheng, Fawang Liu, Ian Turner, and Vo Anh · 2008
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Lévy processes and stochastic calculus
David Applebaum · 2009
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Finite element method for the space and time fractional Fokker-Planck equation
Weihua Deng · 2009
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Estimating divergence functionals and the likelihood ratio by convex risk minimization
XuanLong Nguyen, Martin J Wainwright, and Michael I Jordan · 2010
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Approximate Gaussian process inference for the drift function in stochastic differential equations
Andreas Ruttor, Philipp Batz, and Manfred Opper · 2013
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An introduction to stochastic dynamics
Jinqiao Duan · 2015
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Fokker-Planck equations for stochastic dynamical systems with symmetric Lévy motions
Ting Gao, Jinqiao Duan, and Xiaofan Li · 2016
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Sparse learning of stochastic dynamical equations
Lorenzo Boninsegna, Feliks Nüske, and Cecilia Clementi · 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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Xiaoli Chen, Jinqiao Duan, and George Em Karniadakis · 2019
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Most probable dynamics of a genetic regulatory network under stable Lévy noise
Variational inference for stochastic differential equations
Manfred Opper · 2019
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fpinns: Fractional physics-informed neural networks
Guofei Pang, Lu Lu, and George Em Karniadakis · 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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Guofei Pang, Marta D’Elia, Michael Parks, and George Em Karniadakis · 2020
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Solving Fokker–Planck equation using deep learning
Yong Xu, Hao Zhang, Yongge Li, Kuang Zhou, Qi Liu, and Jürgen Kurths · 2020
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Xiaoli Chen, Fengyan Wu, Jinqiao Duan, Jürgen Kurths, and Xiaofan Li · 2019
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Liu Yang, Constantinos Daskalakis, and George Em Karniadakis · 2020
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