Nonlinear System Identification: Learning While Respecting Physical Models Using a Sequential Monte Carlo Method

The modern world contains an immense number of different and interacting systems, from the evolution of weather systems to variations in the stock market, autonomous vehicles interacting with their environment, and the spread of diseases. For society to function, it is essential to understand the behavior of the world so that informed decisions can be made that are based on likely future outcomes. For instance, consider the spread of a new disease such as COVID-19 coronavirus. It is of great importance to be able to predict the number of people that will be infected at different points in time to ensure that appropriate health-care facilities are available. It is also of interest to be able to make decisions based on accurate information to best attenuate the spread of disease. Moreover, understanding specific attributes of a disease-such as the incubation time and number of unreported cases-and how certain we are about this knowledge are also crucial.