Complex systems consist of a large number of smaller entities that interact with each other usually in a nonlinear and stochastic manner. Examples of complex systems can be diverse including, but not limited to, coupled neurons in the brain, spatially distributed interacting systems like the movement of tectonic plates in a planet, transportation network of a large metropolitan, online social networks like Twitter and Facebook, and the ocean-atmosphere coupling in the climate system. Predicting phenomena such as brain epilepsy, climate change and global warming, pandemics, failure of networks involving distributed computing, power or transportation, species extinction in biological ecosystems, earthquakes, bio-mimetic flows and fluid-structure interactions, viral social media posts, forecasting financial crisis, crowd management etc.; these require a deeper understanding of the overall dynamics of the associated multi-physics systems and a complex system approach to investigate it. Mathematical models of such systems are complex, are typically nonlinear and stochastic and involve modeling the coupling between the interacting individual systems. The traditional reductionist approach that builds an understanding of the individual components, is not suitable for analyzing the collective behaviour. This necessitates the development of new techniques and approaches that have come to be known collectively as complex systems approach.
This is a rapidly emerging interdisciplinary field that enables bridging the gap between fundamental knowledge and mathematical models with the empirical observations as well as copious dataset available on account of the advent of new technological innovations that were unthinkable even a few years ago. The identification, organization and analysis of such data need to draw on the methods of data mining, artificial intelligence, neural nets and deep learning algorithms. The efficient use of this data in conjunction with the methods of probabilistic and causal analysis can lead to significant improvements in the construction of realistic models, as well as in the prediction of catastrophic events such as earthquakes, fluid structure interaction problems, power grid collapses, stock market collapses, and pandemics of disease that can occur in such systems.
The impact of these technical skills has the potential to directly address global challenges arising from human-nature interactions such as, climate change, pandemics, mass migration and ecological disorders, together with the possibility of harnessing technology towards growth and the improvement of life and the environment.
Program Overview
The aim of the proposed program is to introduce students to new techniques and tools for mathematical modelling and analysis of complex dynamical systems and to investigate some of the challenging dynamical problems in climate science, neuroscience, biological systems, Multiphysics systems and active flows, that are the focus of current research worldwide. In addition to enhancing the fundamental understanding of the universal features, which contribute to similar phenomena that occur across a diversity of systems, the effort could also translate into delivering technology which is useful in industrial and societal contexts.
Structure of the Program
The primary objectives are to train students
â— In building network based mathematical models for large scale complex dynamical systems using observational data and use the new theories of complex networks for analysis
â— In theories of nonlinear dynamical systems that enables analysis of complex systems which are inherently nonlinear
â— In high performance computing skills and data analysis
To achieve these objectives, the course curriculum consists of three compulsory core courses
(a) one from Complex Networks basket that introduces students to complex networks analysis
(b) one from Nonlinear Dynamics basket that exposes students on this subject
(c) one from a select set of Mathematics and Numerical Techniques courses. The courses have been selected to ensure that students can cater to be trained in appropriate skill sets that will be more suitable for their project.
The electives are to be selected from a basket of carefully curated courses that encompass the interdisciplinary nature of the program. The electives can be selected from courses on Data Science, High performance computing, as well as a mix of elective courses applicable to diverse engineering fields, which will enable the students to combine the traditional skills with the new approaches of complex dynamical systems.
