Parameter estimation in discrete or continuous deterministic cell cycle models is challenging for several reasons, including the nature of what can be observed, and the accuracy and quantity of those observations. The challenge is even greater for stochastic models, where the number of simulations and amount of empirical data must be even larger to obtain statistically valid parameter estimates. The two main contributions of this work are (1) stochastic model parameter estimation based on directly matching multivariate probability distributions, and (2) a new quasi-Newton algorithm class QNSTOP for stochastic optimization problems. QNSTOP directly uses the random objective function value samples rather than creating ensemble statistics. QNSTOP is used here to directly match empirical and simulated joint probability distributions rather than matching summary statistics. Results are given for a current state-of-the-art stochastic cell cycle model of budding yeast, whose predictions match well some summary statistics and one-dimensional distributions from empirical data, but do not match well the empirical joint distributions. The nature of the mismatch provides insight into the weakness in the stochastic model.

Detailed molecular simulations, ranging from the deposition of inorganic thin films to polymerization reactions, describe the position of each atom or molecule. These simulations have high computational requirements and they produce high dimensional data. On the other hand, simple models that describe the dependence of overall material properties on process conditions are needed to design and optimize processes and it is difficult to generate these types of models from the molecular simulation data. We present an algorithm to compute a simple dynamic model for the Kinetic Monte Carlo (KMC) simulation of a thin film deposition process by using principal component analysis (PCA), self organizing map (SOM) and cell-to-cell mapping.