Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations

Nanshan, Muye; Zhang, Nan; Xun, Xiaolei; Cao, Jiguo

doi:10.1016/j.csda.2022.107483

Cited by 3 publications

(5 citation statements)

References 49 publications

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“…Ordinary differential equations are widely used in modeling complex dynamic systems. For high-dimensional ODE models with a large number of differential equations, it is still challenging literature to estimate the ODE parameters and identify the sparse structure of the ODE model [20][21].…”

Section: Introductionmentioning

confidence: 99%

Application of linear ordinary differential equations to the stability control of long time lag networks

Yao

2023

Applied Mathematics and Nonlinear Sciences

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Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (< 1.0e − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be T * = 0.52, T 1 = 0.71 and T 2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.

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Section: Introductionmentioning

confidence: 99%

Application of linear ordinary differential equations to the stability control of long time lag networks

Yao

2023

Applied Mathematics and Nonlinear Sciences

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“… 2007 ; Cao and Ramsay 2007 ; Nanshan et al. 2022 ). It provides a nested optimization procedure to iteratively update the estimates of the latent processes regularized by their adherence to the differential equations.…”

Section: Introductionmentioning

confidence: 99%

“… 2007 ; Cao and Ramsay 2007 ; Qi and Zhao 2010 ; Nanshan et al. 2022 ), and Bayesian methods (Huang et al. 2006 ; Zhang et al.…”

Section: Introductionmentioning

confidence: 99%

A Joint estimation approach to sparse additive ordinary differential equations

2022

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Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs where observations are allowed to be non-Gaussian. The new method is unified with existing collocation methods by considering the likelihood, ODE fidelity and sparse regularization simultaneously. We design a block coordinate descent algorithm for optimizing the non-convex and non-differentiable objective function. The global convergence of the algorithm is established. The simulation study and two applications demonstrate the superior performance of the proposed method in estimation and improved performance of identifying the sparse structure.

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“…Parameter estimation for ODEs from noisy observations, also known as system identification, remains a challenging task in the statistical literature. Many methods have been developed including the nonlinear least squares (Biegler et al, 1986), the two-stage collocation methods (Varah, 1982;Liang and Wu, 2008;Lu et al, 2011;Brunel et al, 2014;Wu et al, 2014;Dattner and Klaassen, 2015;Brunton et al, 2016;Chen et al, 2017;Dai and Li, 2021), the parameter cascading methods (Ramsay et al, 2007;Cao and Ramsay, 2007;Qi and Zhao, 2010;Nanshan et al, 2022), and Bayesian methods (Huang et al, 2006;Zhang et al, 2017). Based on their different treatment of the differential equations, we summarize them into three categories.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Dattner and Klaassen (2015), Chen et al (2017) and Dai and Li (2021) considered an integrated form of the ODEs to address this issue. The third approach is generalized profiling or parameter cascading (Ramsay et al, 2007;Cao and Ramsay, 2007;Nanshan et al, 2022). It provides a nested optimization procedure to iteratively update the estimates of the latent processes regularized by their adherence to the differential equations.…”

Section: Introductionmentioning

confidence: 99%