(602b) Local Estimation and Coarse-Grained Numerics for Stochastic Reaction Models

Reactor design for small scale chemical engineering applications (e.g. catalysis, reactions in cells) necessitates kinetic Monte Carlo dynamic models -- like Gillespie's stochastic simulation algorithm (SSA)-- that account for stochastic fluctuations. Many of these simulation methods are computationally expensive; on the other hand, not all of the information contained in the full simulation is typically needed for practical design purposes. This talk demonstrates how an on-demand, local modeling approach, coupled with the Equation Free computational framework can computationally assist in extracting the relevant details from such simulations.

Specifically, we estimate the parameters of locally affine diffusion processes by designing, executing and processing the output of SSA simulations using maximum likelihood (ML) type estimators. We also demonstrate quantitative techniques for testing the validity of the local diffusion approximation and show how classical numerical methods can be wrapped around the estimated models. The latter issue is useful in applications where one only requires “coarse-grained” information about the system such as equilibrium distributions, effective free energy surfaces, escape times, coarse-grained bifurcations etc. The computational strategies are then modified slightly to deal with concurrent numerical model reduction; here estimation is carried out only on the “slow” components of a process that contains a significant separation of time scales (i.e. a “stiff” problem). Numerical computations based on classical continuum algorithms are then carried out on the reduced system. Our illustrative examples include kinetic mechanisms of the Lotka-Volterra and the Michaelis-Menten types.