J. Nathan Kutz

Alex Mallen, Christoph A. Keller, J. Nathan Kutz

In many scenarios, it is necessary to monitor a complex system via a time-series of observations and determine when anomalous exogenous events have occurred so that relevant actions can be taken. Determining whether current observations are abnormal is challenging. It requires learning an extrapolative probabilistic model of the dynamics from historical data, and using a limited number of current observations to make a classification. We leverage recent advances in long-term probabilistic forecasting, namely {\em Deep Probabilistic Koopman}, to build a general method for classifying anomalies in multi-dimensional time-series data. We also show how to utilize models with domain knowledge of the dynamics to reduce type I and type II error. We demonstrate our proposed method on the important real-world task of global atmospheric pollution monitoring, integrating it with NASA's Global Earth System Model. The system successfully detects localized anomalies in air quality due to events such as COVID-19 lockdowns and wildfires.

Ziyu Lu, Anna J. Li, Alexander E. Ladd et al.

Neural activity forecasting is central to understanding neural systems and enabling closed-loop control. While deep learning has recently advanced the state-of-the-art in the time series forecasting literature, its application to neural activity forecasting remains limited. To bridge this gap, we systematically evaluated eight probabilistic deep learning models, including two foundation models, that have demonstrated strong performance on general forecasting benchmarks. We compared them against four classical statistical models and two baseline methods on spontaneous neural activity recorded from mouse cortex via widefield imaging. Across prediction horizons, several deep learning models consistently outperformed classical approaches, with the best model producing informative forecasts up to 1.5 seconds into the future. Our findings point toward future control applications and open new avenues for probing the intrinsic temporal structure of neural activity.