Variational Dependent Multi-output Gaussian Process Dynamical Systems

2014 ◽  
pp. 350-361 ◽  
Author(s):  
Jing Zhao ◽  
Shiliang Sun
Keyword(s):  
Dynamical Systems ◽  
Gaussian Process

scholarly journals Learning Stable Nonparametric Dynamical Systems with Gaussian Process Regression

2020 ◽  
Vol 53 (2) ◽  
pp. 1194-1199
Author(s):  
Wenxin Xiao ◽  
Armin Lederer ◽  
Sandra Hirche
Keyword(s):  
Dynamical Systems ◽  
Gaussian Process ◽  
Gaussian Process Regression

Multi-task and multi-kernel Gaussian process dynamical systems

2017 ◽  
Vol 66 ◽  
pp. 190-201 ◽  
Author(s):  
Dimitrios Korkinof ◽  
Yiannis Demiris
Keyword(s):  
Dynamical Systems ◽  
Gaussian Process

scholarly journals Numerical method for parameter inference of systems of nonlinear ordinary differential equations with partial observations

2021 ◽  
Vol 8 (7) ◽  
pp. 210171
Author(s):  
Yu Chen ◽  
Jin Cheng ◽  
Arvind Gupta ◽  
Huaxiong Huang ◽  
Shixin Xu
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Gaussian Process ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Optimization Algorithm ◽  
Nonlinear Ordinary Differential Equations ◽  
Parameter Inference ◽  
Partial Observations ◽  
Deterministic Optimization

Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a method for parameter inference of a system of nonlinear coupled ordinary differential equations with partial observations. Our method combines fast Gaussian process-based gradient matching and deterministic optimization algorithms. By using initial values obtained by Bayesian steps with low sampling numbers, our deterministic optimization algorithm is both accurate, robust and efficient with partial observations and large noise.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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