Robust parameter estimation of chaotic systems

DOI10.3934/ipi.2019053zbMath1437.37112OpenAlexW2981266848MaRDI QIDQ2282743

Heikki Haario, Vladimir Shemyakin, Sebastian Springer, Leonid V. Kalachev, Denis Shchepakin

Publication date: 19 December 2019

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/ipi.2019053

zbMATH Keywords

stochastic optimizationparameter estimationMonte CarloMarkov chainchaotic dynamical systemsBayesian inference

Mathematics Subject Classification ID

Bayesian inference (62F15) Monte Carlo methods (65C05) Identification in stochastic control theory (93E12) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Time series analysis of dynamical systems (37M10) Complex behavior and chaotic systems of ordinary differential equations (34C28) Robust parameter designs (62K25) General topics in computing methodologies (68U01) Parametric inference and fuzziness (62F86) Computational methods for attractors of dynamical systems (37M22)

Related Items

Statistical approach for parameter identification by Turing patterns, A Bayesian Approach to Modeling Biological Pattern Formation with Limited Data, Data based quantification of synchronization, Bayesian system ID: optimal management of parameter, model, and measurement uncertainty

Cites Work

• Parameter identification of chaotic systems using improved differential evolution algorithm
• Differential evolution. A practical approach to global optimization. With CD-ROM.
• Differential evolution. In search of solutions.
• Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems
• Differential evolution -- a simple and efficient heuristic for global optimization over continuous spaces
• Anti-control of chaos in rigid body motion
• An equation for continuous chaos
• Efficient MCMC for climate model parameter estimation: parallel adaptive chains and early rejection
• Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation
• ‘Intractable and unsolved’: some thoughts on statistical data assimilation with uncertain static parameters
• A chaotic attractor from Chua's circuit
• Deterministic Nonperiodic Flow
• A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration
• DYNAMICAL ANALYSIS OF A NEW CHAOTIC ATTRACTOR
• Computational Intelligence
• An adaptive Metropolis algorithm
• A method to determine the dimension of long-time dynamics in multi-scale systems