Unusual patterns appear to be becoming the new normal across natural, engineered and human systems. Weather extremes from heat waves and floods to hurricanes and tornadoes appear to be growing more intense, frequent and geographically pervasive in terms of their consequences. Global security and technological hazards, ranging from terror attacks and radioactive leaks to cyber-security have become among the top societal concerns. Globalization, intellectual protection, privacy, and homeland security concerns along with fierce competition to survive have led to additional stresses on the global supply chain and transportation networks. Aging or even newly-built infrastructures are showing signs of decay or larger-than-design stress from geophysical or human causes. Even the human population, from the Arab world to Europe, appears to be exhibiting increasing propensity to exhibit emergent behavior fueled by geopolitical, economic and technological impetus. The world has grown interconnected as never before where no one system or collection of systems can be effectively viewed in isolation.
Fundamental breakthroughs are needed in mathematical, computational and decision science methods geared towards detecting and predicting rare events or unusual patterns, especially from heterogeneous and multi-source datasets, particularly within complex systems. Complex systems as defined in this context refer to complexity in the unobserved data generation processes as well as the observed data. The data generation processes may be potentially nonlinear, even chaotic, non-stationary, and typically multi-dimensional (e.g., space and time). Recurrence patterns of extremes, rare events or anomalies may be hypothesized to have deterministic or stochastic patterns. The data from such systems are likely to exhibit complex dependence structures, including proximity-based correlations (e.g., temporal or spatial autocorrelations), long-range dependence or long memory processes, nonlinear synchronicity, as well as noise or variability that may be colored, possibly even “1/f”. Furthermore, the data may be massive and streaming, disparate enough to be occasionally difficult to compare directly with each other, but the patterns of the unusual or rare behavior as well as their precursors may be difficult to extract from data. In fact, the data useful for rare events may even be relatively short and few, given the nature and type of noise and the complexity of the generation processes. The processes may be inherently interconnected at multiple scales.
Our research in these areas has focused on national and homeland security as well as climate change, among other multidisciplinary areas such as evaluation of social science theories and models. The aspiration in security applications is on the possibility of extracting actionable predictive insights from elusive indicators of threat which may be present in large data sets. Our focus on climate change is on understanding or projecting extreme events and abrupt change, or low probability but high impact events, from massive volume data generated from large-scale computational models as well as remote or in-situ sensors across the world at multiple scales in space and time. Our methodological approaches have been interdisciplinary, blending concepts and leveraging methods from statistics and econometrics, data mining and machine learning in computer science, complex networks and graphical models, nonlinear dynamics and signal processing in physics and engineering, as well as translational insights developed across multiple domains in the sciences and engineering.