Dynamical system modeling with probabilistic finite state automata

Abstract

Discrete dynamical systems are widely used in a variety of scientific and engineering applications, such as electrical circuits, machine learning, meteorology and neurobiology. Modeling these systems involves performing statistical analysis of the system output to estimate the parameters of a model so it can behave similarly to the original system. These models can be used for simulation, performance analysis, fault detection, among other applications. The current work presents two new algorithms to model discrete dynamical systems from two categories (synchronizable and non-synchronizable) using Probabilistic Finite State Automata (PFSA) by analyzing discrete symbolic sequences generated by the original system and applying statistical methods and inference, machine learning algorithms and graph minimization techniques to obtain compact, precise and efficient PFSA models. Their performance and time complexity are compared with other algorithms present in literature that aim to achieve the same goal by applying the algorithms to a series of common examples.