Researchers at the University of Toronto Institute of Aerospace Studies (UTIAS) have made a significant step towards enabling reliable predictions of complex dynamical systems when there are many uncertainties in the available data or missing information. This work could have numerous applications ranging from predicting the performance of aircraft engines to forecasting changes in global climate or the spread of viruses.
In a recent paper published in Nature, Professor Prasanth B. Nair (UTIAS) and Kevin Course (UTIAS PhD candidate) introduce a new machine learning algorithm that surmounts the real-world challenge of imperfect knowledge about system dynamics. This computer-based mathematical modelling approach is used for problem solving and better decision making in complex systems, where many components interact with each other.
“For the first time, we are able to apply state estimation to problems where we don’t know the governing equations, or the governing equations have a lot of missing terms,” says Course, the first author of the new paper.
“In contrast to standard techniques, which usually require a state estimate to infer the governing equations and vice-versa, our method learns the missing terms in the mathematical model and a state estimate simultaneously.”
State estimation, also known as data assimilation, refers to the process of combining observational data with computer models to estimate the current state of a system. Traditionally it requires strong assumptions about the type of uncertainties that exist in a mathematical model.