Machine learning of memory functions of marginal stochastic processes
When simulating multi-dimensional stochastic processes, such as biomolecular reaction networks, one is often interested only in a subset of the process components, e.g. only a subset of the chemical species of the reaction network.The marginal stochastic process describing only the components of interest will not be Markovian. The memory terms governing either the probability distribution or the process equation do not have a simple expression.
The goal of this master thesis is to use machine-learning techniques to learn the behavior of the memory functions. This will probably involve model-based tools such as Gaussian process regression. Alternatively, an approach based on Deep Learning might be interesting. This is a purely mathematical application of machine learning, because the ‘ground truth’ is, in principle, known exactly.
Requirements: Standard machine learning techniques, stochastic processes, programming skills.