Systems of ordinary differential equations (ODEs) are often used to model the dynamics of complex biological pathways. This is so since bio-chemical reactions can be converted into ODEs in a systematic fashion. However, large systems of ODEs are impossible to solve and one must resort to numerical simulations. Many analysis tasks will require a large number of numerical simulations. Further, these analysis tasks can be validated using experimental data with very limited precision. Hence we are developing an approximation scheme by which, through sampling (of a probability distribution of initial states), numerical simulations and simple counting one can approximate the dynamics defined by a systems of ODEs as probabilistic finite state transition system, or equivalently, a Markov chain.

In fact, we represent this Markov chain in a factorized form as a dynamic Bayesian network. We then perform analysis tasks using this approximate and compact representation using standard techniques that have been developed in the setting probabilistic graphical models. We are also in the process of constructing a formal verification technique based on this representation. We also have plans for developing an application specific hardware platform that will support the construction of the approximation as well as the subsequent analysis tasks.