Complex systems are encountered in many applications including sustainable transportation, power grids, fusion and other alternative energy strategies, and biological systems. Addressing many of our most pressing challenges, related to the increasing demand for energy and transportation, requires the use of scalable data and informatics towards enhancing our understanding of complex systems. As we move to increasingly complex systems with an expanded feature space, new mathematical approaches are needed to understand the impact on system behavior of the interplay between subsystems of different physical processes, at different scales, or between decision points in an engineered system. Complex systems consist of diverse entities that interact both in space and time. Referring to something as complex implies that it consists of interdependent, diverse entities that are connected with each other and can adapt to changes, i.e., they can respond to their local and global environment. For example, the US electricity grid is one of the world’s largest complex systems consisting of a dynamic collection of diverse, interacting components that can adapt. These components are also interdependent and operate under an enormous range of physical, reliability, economic, social, and political constraints that need to be satisfied over time scales ranging from seconds, for closed-loop control, to decades, for transmission siting and construction. Another example of a complex system is the transportation consisting of various diverse and interdependent entities, e.g., vehicles that are connected and adapt appropriately resulting in specific traffic patterns.
One of the most fascinating phenomena in complex systems is emergence. Emergence refers to the spontaneous creation of order and functionality from the bottom up. Wherever we see complex systems in the physical world, we see emergent patterns at every level, both in structure and functionality. Emergence occurs without a central planner, from the bottom up, based on the interaction of the individual entities in a system. As a simple example, from the natural world, of how emergence arises, we can consider the flying patterns created by a flock of birds following three simple rules: (1) stay close but don’t bomb into birds around me, (2) fly as fast as birds near me, and (3) move towards the center of the group. The fact that a rule applied locally leads to a macro-level property is what is meant by the term bottom up. Another example of a bottom-up emergent phenomenon is the traffic jam resulting from a specific sequence of vehicle-to-vehicle and vehicle-to-infrastructure interactions. Complex systems also produce dynamics such as phase transitions, which are sometimes called tipping points. Phase transitions occur when forces within a system reach what is called a critical threshold. Once this happens, the state of the system changes, often drastically.
The overarching goal of my research is to enhance understanding of complex systems and establish a holistic, multifaceted approach using scalable data and informatics to developing rigorous mathematical models and decentralized control algorithms for making complex systems able to realize how to improve their performance over time while interacting with their environment. The research hypothesis is that if we could develop mathematical models to characterize emergence, then we would be able to designate the rules for the interactions of the individual entities so that the desired emergent phenomena would occur. Furthermore, if such mathematical models were available, then we could develop the algorithms to predict the tipping points of complex systems. Enhancing our understanding of complex systems will have a major impact on improving the efficiency in various applications related to connected and automated vehicles, sociotechnical systems, energy and sustainable systems, smart cities and connected communities.