Journal of Computational Dynamics最新文献

Subgradient algorithm for computing contraction metrics for equilibria 计算平衡点收缩度量的亚梯度算法

IF 1

Journal of Computational Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jcd.2022030

P. Giesl, S. Hafstein, Magnea Haraldsdottir, D. Thorsteinsson, C. Kawan

引用次数: 4

Approximated exponential integrators for the stochastic Manakov equation 随机Manakov方程的近似指数积分器

IF 1

Journal of Computational Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jcd.2023002

A. Berg, David Cohen, G. Dujardin

引用次数: 1

Dynamical optimal transport of nonlinear control-affine systems 非线性控制-仿射系统的动态最优输运

IF 1

Journal of Computational Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jcd.2023006

Karthik Elamvazhuthi, Siting Liu, Wuchen Li, S. Osher

引用次数: 1

Convergence of the vertical gradient flow for the Gaussian Monge problem 高斯蒙日问题中垂直梯度流的收敛性

Journal of Computational Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jcd.2023008

Erik Jansson, Klas Modin

引用次数: 0

Friction-adaptive descent: A family of dynamics-based optimization methods 摩擦自适应下降:一类基于动力学的优化方法

Journal of Computational Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jcd.2023007

Katerina Karoni, Benedict Leimkuhler, Gabriel Stoltz

{"title":"Friction-adaptive descent: A family of dynamics-based optimization methods","authors":"Katerina Karoni, Benedict Leimkuhler, Gabriel Stoltz","doi":"10.3934/jcd.2023007","DOIUrl":"https://doi.org/10.3934/jcd.2023007","url":null,"abstract":"We describe a family of descent algorithms which generalizes common existing schemes used in applications such as neural network training and more broadly for optimization of smooth functions–potentially for global optimization, or as a local optimization method to be deployed within global optimization schemes. By introducing an auxiliary degree of freedom we create a dynamical system with improved stability, reducing oscillatory modes and accelerating convergence to minima. The resulting algorithms are simple to implement, and convergence can be shown directly by Lyapunov's second method.Although this framework, which we refer to as friction-adaptive descent (FAD), is fairly general, we focus most of our attention on a specific variant: kinetic energy stabilization (which can be viewed as a zero-temperature Nosé–Hoover scheme with added dissipation in both physical and auxiliary variables), termed KFAD (kinetic FAD). To illustrate the flexibility of the FAD framework we consider several other methods. In certain asymptotic limits, these methods can be viewed as introducing cubic damping in various forms; they can be more efficient than linearly dissipated Hamiltonian dynamics (LDHD).We present details of the numerical methods and show convergence for both the continuous and discretized dynamics in the convex setting by constructing Lyapunov functions. The methods are tested using a toy model (the Rosenbrock function). We also demonstrate the methods for structural optimization for atomic clusters in Lennard–Jones and Morse potentials. The experiments show the relative efficiency and robustness of FAD in comparison to LDHD.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"242 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136257203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Conditioned Wiener processes as nonlinearities: A rigorous probabilistic analysis of dynamics 作为非线性的条件维纳过程:动力学的严格概率分析

IF 1

Journal of Computational Dynamics Pub Date : 2022-09-23 DOI: 10.3934/jcd.2023004

K. Mischaikow, Cameron Thieme

引用次数: 0

Computing connecting orbits to infinity associated with a homoclinic flip bifurcation 计算与同斜翻转分岔相关的连接轨道至无穷远

IF 1

Journal of Computational Dynamics Pub Date : 2022-06-24 DOI: 10.3934/jcd.2020020

A. Giraldo, B. Krauskopf, H. Osinga

{"title":"Computing connecting orbits to infinity associated with a homoclinic flip bifurcation","authors":"A. Giraldo, B. Krauskopf, H. Osinga","doi":"10.3934/jcd.2020020","DOIUrl":"https://doi.org/10.3934/jcd.2020020","url":null,"abstract":"We consider the bifurcation diagram in a suitable parameter plane of a quadratic vector field in begin{document}$ mathbb{R}^3 $end{document} that features a homoclinic flip bifurcation of the most complicated type. This codimension-two bifurcation is characterized by a change of orientability of associated two-dimensional manifolds and generates infinite families of secondary bifurcations. We show that curves of secondary begin{document}$ n $end{document} -homoclinic bifurcations accumulate on a curve of a heteroclinic bifurcation involving infinity. We present an adaptation of the technique known as Lin's method that enables us to compute such connecting orbits to infinity. We first perform a weighted directional compactification of begin{document}$ mathbb{R}^3 $end{document} with a subsequent blow-up of a non-hyperbolic saddle at infinity. We then set up boundary-value problems for two orbit segments from and to a common two-dimensional section: the first is to a finite saddle in the regular coordinates, and the second is from the vicinity of the saddle at infinity in the blown-up chart. The so-called Lin gap along a fixed one-dimensional direction in the section is then brought to zero by continuation. Once a connecting orbit has been found in this way, its locus can be traced out as a curve in a parameter plane.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"31 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87250152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Numerical dynamics of integrodifference equations: Forward dynamics and pullback attractors 积分差分方程的数值动力学:正向动力学和回拉吸引子

IF 1

Journal of Computational Dynamics Pub Date : 2022-05-11 DOI: 10.3934/jcd.2023003

H. Huynh, P. Kloeden, Christian Potzsche

引用次数: 0

Review on contraction analysis and computation of contraction metrics 收缩分析与收缩度量计算综述

IF 1

Journal of Computational Dynamics Pub Date : 2022-03-02 DOI: 10.3934/jcd.2022018

P. Giesl, S. Hafstein, C. Kawan

引用次数: 9

A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards' equation Kirchhoff的数值解的基于正交的格式变换了Richards的方程