Simulation of Stochastic Hybrid Systems using probabilistic boundary detection and adaptive time stepping

Modeling and simulation of biochemical systems are important tasks because they can provide insights into complicated systems where traditional experimentation is expensive or impossible. Stochastic Hybrid Systems (SHS) are an ideal modeling paradigm for biochemical systems because they combine continuous and discrete dynamics in a stochastic framework. In this work we develop an advanced simulation method for SHS that explicitly considers switching and reflective boundaries and uses probabilistic crossing detection methods to improve accuracy. We also develop an adaptive time stepping algorithm for SHS to improve efficiency. We present case studies for a water/electrolyte balance system in humans and a biodiesel production model. Simulation results are presented to demonstrate the accuracy and efficiency of the improved simulation techniques.