Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Efficient stochastic sensitivity analysis of discrete event systems
Journal of Computational Physics
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Journal of Computational Physics
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
SIAM Journal on Scientific Computing
Bioinformatics
A new clustering technique for function approximation
IEEE Transactions on Neural Networks
Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
Journal of Scientific Computing
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In this work, the problem of representing a stochastic forward model output with respect to a large number of input parameters is considered. The methodology is applied to a stochastic reaction network of competence dynamics in Bacillus subtilis bacterium. In particular, the dependence of the competence state on rate constants of underlying reactions is investigated. We base our methodology on Polynomial Chaos (PC) spectral expansions that allow effective propagation of input parameter uncertainties to outputs of interest. Given a number of forward model training runs at sampled input parameter values, the PC modes are estimated using a Bayesian framework. As an outcome, these PC modes are described with posterior probability distributions. The resulting expansion can be regarded as an uncertain response function and can further be used as a computationally inexpensive surrogate instead of the original reaction model for subsequent analyses such as calibration or optimization studies. Furthermore, the methodology is enhanced with a classification-based mixture PC formulation that overcomes the difficulties associated with representing potentially nonsmooth input-output relationships. Finally, the global sensitivity analysis based on the multiparameter spectral representation of an observable of interest provides biological insight and reveals the most important reactions and their couplings for the competence dynamics.