Balanced model reduction of partially observed Langevin equations: an averaging principle

DOI10.1080/13873954.2011.576517zbMath1302.82081OpenAlexW1986676597MaRDI QIDQ5411559

Carsten Hartmann

Publication date: 24 April 2014

Published in: Mathematical and Computer Modelling of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10.1080/13873954.2011.576517

zbMATH Keywords

optimal predictionaveraging principlebalanced truncationmodel order reductionstochastic Langevin equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) System structure simplification (93B11) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic systems in control theory (general) (93E03)

Related Items

Application of adaptive multilevel splitting to high-dimensional dynamical systems ⋮ Control strategies for the Fokker−Planck equation ⋮ Homogenization for generalized Langevin equations with applications to anomalous diffusion ⋮ Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing ⋮ Balanced model order reduction for linear random dynamical systems driven by Lévy noise ⋮ Optimization based model order reduction for stochastic systems ⋮ Optimal control of multiscale systems using reduced-order models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Scattering in the nonlinear Lamb system
• Balancing for nonlinear systems
• Markov chains and stochastic stability
• Molecular modeling and simulation. An interdisciplinary guide
• Controllability of stochastic linear systems
• Optimal prediction with memory
• Fractional kinetics in Kac-Zwanzig heat bath models
• On the Poisson equation and diffusion approximation. III
• Balanced Truncation of Linear Second-Order Systems: A Hamiltonian Approach
• A coarse‐grained molecular dynamics model for crystalline solids
• All optimal Hankel-norm approximations of linear multivariable systems and theirL,^∞-error bounds†
• A phonon heat bath approach for the atomistic and multiscale simulation of solids
• ON RATE OF MIXING AND THE AVERAGING PRINCIPLE FOR HYPOELLIPTIC STOCHASTIC DIFFERENTIAL EQUATIONS
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• A classification of the second order degenerate elliptic operators and its probabilistic characterization
• Synthesis of minimum roundoff noise fixed point digital filters
• Singular perturbation approximation of balanced systems
• Optimal prediction and the Mori–Zwanzig representation of irreversible processes
• MODEL REDUCTION FOR FLUIDS, USING BALANCED PROPER ORTHOGONAL DECOMPOSITION
• Statistical Mechanics of Assemblies of Coupled Oscillators