ICTS

Chaos theory and topology in the past few decades have given many useful insights to understand data generated by nonlinear systems. In 1980, Packard et al. observed that the state-space of a nonlinear system could be reconstructed from a time-series created by it and this opened up a possibility of associating geometrical and topological structures with observed data. Standard topological modeling methods broadly fall into two categories: (i) Atlas based methods that approximate dynamics in overlapping local charts of the state-space, and (ii) Global methods that find equations valid for the entire state-space. Since Atlas model needs neighborhoods that are well populated, it works well when data is plenty and densely sampled (e.g., biomedical measurements).  In some cases,  global models are a good choice when the time series is sparse but can be smoothened without affecting the qualitative data profile (e.g., crop data in seasons, plague data for few years).  I will discuss (i) prediction capabilities of a new Atlas model for analyzing a time-series with recurring patterns, and  (ii) opportunities of global models in retro-modeling and its challenges in atmospheric data analysis.