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Page 9144 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
A variable timestepping method for the integration of stochastic differential equations is presented.  ...  for stochastic differential equations.  ... 

Neural Networks with Cheap Differential Operators [article]

Ricky T. Q. Chen, David Duvenaud
2019 arXiv   pre-print
equation for training stochastic differential equation models.  ...  the divergence.  ...  Learning Stochastic Differential Equations by Fokker-Planck Matching Generalizing ordinary differential equations to contain a stochastic term results in stochastic differential equations (SDE), a special  ... 
arXiv:1912.03579v1 fatcat:gbwmog7bizcnvgu7dbx5h6v56q

Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review

Ana Bela Cruzeiro
2020 Water  
The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated  ...  Different related probabilistic methods to study the Navier–Stokes equation are discussed.  ...  These kind of systems are natural generalizations of second order ordinary differential equations to the stochastic setting. the Euler equation, Brenier looked for probability measures P on the path space  ... 
doi:10.3390/w12030864 fatcat:qjmlsodcljdkjpjqhutgweeb6u

Page 5818 of Mathematical Reviews Vol. , Issue 98I [page]

1998 Mathematical Reviews  
(F-ORLN; Orléans) Numerical methods for backward stochastic differential equations. Numerical methods in finance, 232-244, Publ. Newton Inst., Cambridge Univ. Press, Cambridge, 1997.  ...  iterative technique for one-dimensional stochastic differential equations.  ... 

Scalable Gradients for Stochastic Differential Equations [article]

Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen, David Duvenaud
2020 arXiv   pre-print
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations.  ...  In addition, we combine our method with gradient-based stochastic variational inference for latent stochastic differential equations.  ...  We also thank Guodong Zhang, Kevin Swersky, Chris Rackauckas, and members of the Vector Institute for helpful comments on an early draft of this paper.  ... 
arXiv:2001.01328v6 fatcat:k6q44v5w5zg4jkrdn2wm32mrdi

Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equation [article]

Arno Solin, Ella Tamir, Prakhar Verma
2021 arXiv   pre-print
Simulation-based techniques such as variants of stochastic Runge-Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning.  ...  Stochastic Runge-Kutta relies on the use of sampling schemes that can be inefficient in high dimensions.  ...  We also wish to thank the anonymous reviewers for their comments on our manuscript, and Çagatay Yıldız and Xuechen Li for providing useful details on the MOCAP experiment.  ... 
arXiv:2110.15739v1 fatcat:fafoab423fhpzi4u4u7r5oxs64

Page 4117 of Mathematical Reviews Vol. , Issue 80J [page]

1980 Mathematical Reviews  
For the authors, stochastic quantization means the passage from scalar Euler-Lagrange equations to operator equations describing stochastic dynamics, not E. Nelson’s approach to quantum me- chanics.  ...  The outstanding property of the Lebesgue measure is its relation to ordinary differentiation, which is combined with other properties.  ... 

Page 3536 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
ISBN 0-7503-0530-4; 0-7503-0531-2 This book gives a simple and direct introduction to the powerful methods of Lie for the solution of ordinary and partial differen- tial equations.  ...  for partial differential equations.  ... 

Stochastic embedding of dynamical systems [article]

Jacky Cresson
2005 arXiv   pre-print
In this paper, we develop a theory for the stochastic embedding of ordinary differential equations. We apply this method to Lagrangian systems.  ...  Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics.  ...  The second part of this article deals specifically with the definition of a stochastic embedding procedure for ordinary differential equations.  ... 
arXiv:math/0509713v1 fatcat:l3r67wwlkrb2nmdmzgyld347f4

Three Ways to Solve Partial Differential Equations with Neural Networks – A Review [article]

Jan Blechschmidt, Oliver G. Ernst
2021 arXiv   pre-print
, methods based on the Feynman-Kac formula and methods based on the solution of backward stochastic differential equations.  ...  Neural networks are increasingly used to construct numerical solution methods for partial differential equations.  ...  In this section and the next, we consider the solution by neural network methods of a class of partial differential equations which arise as the backward Kolmogorov equation of stochastic processes known  ... 
arXiv:2102.11802v2 fatcat:xc647il5q5f4baixs74arorbbm

Analytical and Numerical Treatments of Conservative Diffusions and the Burgers Equation

Dimiter Prodanov
2018 Entropy  
stochastic geodesic equation for the drift.  ...  The resulting statistical description obeys the Fokker-Planck equation of the probability density of the differential system, which can be readily estimated from simulations of the random paths.  ...  The author would like to acknowledge Stephan LeBohec for critical reading and Laurent Nottale for inspirational discussions.  ... 
doi:10.3390/e20070492 pmid:33265582 fatcat:6fhqlu7pqvh7jnsvwvrzkd3oui

Numerical treatment of stochastic heroin epidemic model

M. Rafiq, Ali Raza, M. Usman Iqbal, Zubair Butt, Hafiza Anum Naseem, M. Ali Akram, M. Kamran Butt, Adil Khaliq, Qurat-ul-Ain, Shamrash Azam
2019 Advances in Difference Equations  
In 2013, Haung and Liu in [9] found that, under specific condition, the delay differential equation model can be converted into an ordinary differential equation model which resembles the renowned SIR  ...  The effect of reproduction number has also been observed in the stochastic heroin epidemic model. We have developed some stochastic explicit and implicitly driven explicit methods for this model.  ...  Acknowledgements We would like to thank the referees for their valuable comments. Funding No funding is available for this research project.  ... 
doi:10.1186/s13662-019-2364-1 fatcat:bfzegn4rvrghrdwyxb6zb7x2rq

Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes [article]

Nicolas Macris, Raffaele Marino
2020 arXiv   pre-print
In this contribution we study variants of the deep networks by using different discretizations schemes of the stochastic differential equation.  ...  The main idea is to construct a deep network which is trained from the samples of discrete stochastic differential equations underlying Kolmogorov's equation.  ...  backward Kolmogorov equations and forward-backward stochastic differential equations (FBSDE).  ... 
arXiv:2012.07747v2 fatcat:pwblhbq7brdrnaifa7jzdzoag4

Learning Continuous-Time Dynamics by Stochastic Differential Networks [article]

Yingru Liu, Yucheng Xing, Xuewen Yang, Xin Wang, Jing Shi, Di Jin, Zhaoyue Chen
2021 arXiv   pre-print
embeds the complicated dynamics of the sporadic time series by neural Stochastic Differential Equations (SDE).  ...  To solve the above problem, we apply Variational Bayesian method and propose a flexible continuous-time stochastic recurrent neural network named Variational Stochastic Differential Networks (VSDN), which  ...  Related Works Neural Ordinary Differential Equations Neural ODE is first proposed in [8] , where the hierarchical structure of residual network [12] is replaced by an ordinary differential equation  ... 
arXiv:2006.06145v3 fatcat:3tghqlz3hzepvpqos6xv5az7di

Model inference for Ordinary Differential Equations by parametric polynomial kernel regression [article]

David K. E. Green, Filip Rindler
2019 arXiv   pre-print
Using numerical integration techniques, parametric representations of Ordinary Differential Equations can be learnt using Backpropagation and Stochastic Gradient Descent.  ...  This work introduces a parametric polynomial kernel method that can be used for inferring the future behaviour of Ordinary Differential Equation models, including chaotic dynamical systems, from observations  ...  Using numerical integration techniques, parametric representations of Ordinary Differential Equations can be learnt using Backpropagation and Stochastic Gradient Descent.  ... 
arXiv:1908.02105v1 fatcat:slereoipxfgipao4mfnve6emwe
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