A Micro-Macro Acceleration Method for the Monte Carlo Simulation of Stochastic Differential Equations

DOI10.1137/16M1066658zbMath1378.65031arXiv1511.06171MaRDI QIDQ4594904

Przemysław Zieliński, Giovanni Samaey, Kristian Debrabant

Publication date: 27 November 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.06171

zbMATH Keywords

algorithmconvergencestochastic differential equationsnumerical experimententropy optimizationmulti-scale modelingmicro-macro simulationsfinitely extensible nonlinear elastic dumbbellsaccelerated Monte Carlo

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (11)

Projective integration schemes for hyperbolic moment equations ⋮ Discovery of slow variables in a class of multiscale stochastic systems via neural networks ⋮ Convergence of Equation-Free Methods in the Case of Finite Time Scale Separation with Application to Deterministic and Stochastic Systems ⋮ Analysis of a micro-macro acceleration method with minimum relative entropy moment matching ⋮ Variance reduced particle solution of the Fokker-Planck equation with application to rarefied gas and plasma dynamics ⋮ Hierarchical micro-macro acceleration for moment models of kinetic equations ⋮ Parareal computation of stochastic differential equations with time-scale separation: a numerical convergence study ⋮ Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise ⋮ Convergence and stability of a micro-macro acceleration method: linear slow-fast stochastic differential equations with additive noise ⋮ Efficiency of a Micro-Macro Acceleration Method for Scale-Separated Stochastic Differential Equations ⋮ A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Crucial properties of the moment closure model FENE-QE
• A patch that imparts unconditional stability to explicit integrators for Langevin-like equations
• A class of weak second order split-drift stochastic Runge-Kutta schemes for stiff SDE systems
• A numerical closure approach for kinetic models of polymeric fluids: exploring closure relations for FENE dumbbells
• Coarse projective kMC integration: Forward/reverse initial and boundary value problems
• An efficient Newton-Krylov implementation of the constrained runs scheme for initializing on a slow manifold
• B-series analysis of iterated Taylor methods
• Global well-posedness for the microscopic FENE model with a sharp boundary condition
• The heterogeneous multiscale methods
• Second-order accurate projective integrators for multiscale problems
• Stochastic viability of convex sets
• Increasing the real stability boundary of explicit methods
• Weak first- or second-order implicit Runge-Kutta methods for stochastic differential equations with a scalar Wiener process
• Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
• Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis
• Calculation of viscoelastic flow using molecular models: The CONNFFESSIT approach
• Existence of solution for a micro-macro model of polymeric fluid: The FENE model.
• A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws
• Canonical distribution functions in polymer dynamics. I: Dilute solutions of flexible polymers
• Invariance of stochastic control systems with deterministic arguments
• Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise
• New closure approximations for the kinetic theory of finitely extensible dumbbells
• Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations
• Path-space variational inference for non-equilibrium coarse-grained systems
• Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
• Second order Runge-Kutta methods for Stratonovich stochastic differential equations
• Accuracy analysis of acceleration schemes for stiff multiscale problems
• Integrals which are convex functionals
• Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis
• On the Regularity of Solutions to FENE Models
• On the Acceleration of the Multi-Level Monte Carlo Method
• Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations
• THE NUMERICAL STABILITY OF STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE
• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Multilevel Monte Carlo Path Simulation
• A High-Order Asymptotic-Preserving Scheme for Kinetic Equations Using Projective Integration
• Kullback-leibler approximation of spectral density functions
• Stochastic Taylor Expansions for Functionals of Diffusion Processes
• Multiscale Modelling of Complex Fluids: A Mathematical Initiation
• Theoretical Numerical Analysis
• Recovering a function from a finite number of moments
• Duality Relationships for Entropy-Like Minimization Problems
• Variance Reduction for Simulated Diffusions
• Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
• Stochastic Processes and Applications
• Multivariate Density Estimation
• B–Series Analysis of Stochastic Runge–Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values
• Convex Duality and Entropy-Based Moment Closures: Characterizing Degenerate Densities
• On the Convergence of an Efficient Algorithm for Kullback–Leibler Approximation of Spectral Densities
• Diffusion Monte Carlo method: Numerical Analysis in a Simple Case
• Expansion of the global error for numerical schemes solving stochastic differential equations
• Probability

This page was built for publication: A Micro-Macro Acceleration Method for the Monte Carlo Simulation of Stochastic Differential Equations