Koopman Operator-Based Forecasting for Nonstationary Processes from Near-Term, Limited Observational Data

The ongoing COVID-19 pandemic emphasized the need for better data-driven prediction algorithms, capable of ingesting short-term data and performing accurate short-term prediction. Such algorithms would enable e.g. optimization of mask and ventilator supply chains and provide supporting analysis for lockdown/opening decisions.  Beyond COVID-19, the need for such algorithms - that deal effectively with the non-stationary aspects of short-term data - is broad. Here we propose to develop such a class of non-stationary prediction algorithms from the prototype we developed within the DARPA PAI and AIRA Artificial Intelligence Exploration projects and used on prediction of infection cases from COVID-19 and AFRL supplied data on corrosion processes. Current data-driven prediction algorithms largely depend on stationarity assumption. Classical statistical methods based either on frequentist or Bayesian frameworks fit into that category, as do many of the modern machine learning methodologies. The latter can be adapted to non-stationary situations, but suffer from requirements for a large amount of labeled data and/or overfitting. Model-based prediction algorithms have been deployed in COVID-19 pandemic analysis but have proven too reliable on the small number of parameters that need to be fitted from the evolving data causing large uncertainties. Our approach relies on Koopman operator theory (KOT). In contrast with the tools described above, formulating a Koopman operator representation from data does not rely on any stationarity assumptions, a long historical sequence of data, or excessive labeling. The mathematical underpinnings of KOT enable adaptive features, where non-stationary deviations from the current state of the process can be detected based on the spectrum of the operator. The framework also enables creation of models from data on the fly. In prior work we have provided a prototype adaptive prediction algorithm and showed its effectiveness on COVID-19 data – where the feasibility of