Averaging and Sensitivity Analysis for Multiscale Stochastic Reaction Networks

Araz Hashemi
Wright-Patterson Air Force Base

Stochastic reaction networks are widely used to model and analyze the uncertain behavior of many biological and chemical processes.
The large dimension and complexity of such systems make analytic solutions of the probability distributions unobtainable, so simulation algorithms (such as SSA) are employed to estimate expectations of the quantities of interest.
However, when multiscale dynamics are present, such exact simulation methods become inefficient as they only advance the system on the smallest scale.
In such systems, stochastic averaging has been successfully applied to develop approximate algorithms which allow for faster computation.
It is known that the distribution of the exact system converges weakly to the 'averaged' distribution in the limit as the scale disparity tends to infinity.

In this talk, we shall establish the rate of convergence by means of a singular perturbation expansion of the probability measure of the exact system.
Furthermore, our framework identifies the averaged system as a `meta' reaction network, which allows for application of single-scale sensitivity estimation algorithms to the averaged system.
We shall present some new ergodic variants of known algorithms which estimate steady-state sensitivities with lower variance.
We then demonstrate how these algorithms can be adapted to averaged system to give efficient estimates of the sensitivities of the multiscale system.

Presentation (PDF File)

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