Preconditioned Bayesian Regression for Stochastic Chemical Kinetics

Authors:
Alen Alexanderian;Francesco Rizzi;Muruhan Rathinam;Olivier P. Le Maître;Omar M. Knio
Affiliations:
Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA 78712;Department of Mechanical Engineering and Materials Science, Duke University, Durham, USA 27708;Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, USA 21250;LIMSI-CNRS, Orsay Cedex, France 91403;Department of Mechanical Engineering and Materials Science, Duke University, Durham, USA 27708
Venue:
Journal of Scientific Computing
Year:
2014

Citing 11
Cited 0

Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

SIAM Journal on Scientific Computing
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales

Journal of Computational Physics
Multi-Resolution-Analysis Scheme for Uncertainty Quantification in Chemical Systems

SIAM Journal on Scientific Computing
Sparse grid collocation schemes for stochastic natural convection problems

Journal of Computational Physics
An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

SIAM Journal on Numerical Analysis
An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations

Journal of Computational Physics
Spectral Representation and Reduced Order Modeling of the Dynamics of Stochastic Reaction Networks via Adaptive Data Partitioning

SIAM Journal on Scientific Computing
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection

Journal of Scientific Computing
Original article: Application of the Polynomial Chaos Expansion to the simulation of chemical reactors with uncertainties

Mathematics and Computers in Simulation
Multiparameter Spectral Representation of Noise-Induced Competence in Bacillus Subtilis

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We develop a preconditioned Bayesian regression method that enables sparse polynomial chaos representations of noisy outputs for stochastic chemical systems with uncertain reaction rates. The approach is based on the definition of an appropriate multiscale transformation of the state variables coupled with a Bayesian regression formalism. This enables efficient and robust recovery of both the transient dynamics and the corresponding noise levels. Implementation of the present approach is illustrated through applications to a stochastic Michaelis---Menten dynamics and a higher dimensional example involving a genetic positive feedback loop. In all cases, a stochastic simulation algorithm (SSA) is used to compute the system dynamics. Numerical experiments show that Bayesian preconditioning algorithms can simultaneously accommodate large noise levels and large variability with uncertain parameters, and that robust estimates can be obtained with a small number of SSA realizations.