(6hc) Mechanical Programming of Granular Materials in Hydrogels for Tissue-like Behaviors

Future research interests:

Motivation: Optimization models for engineering systems often contain uncertain model parameters due to uncertainties in market forces and the environment, use of surrogate models, and difficulty in measuring parameters accurately. Optimal solutions to models that simply ignore the uncertainty in model parameters can be economically worthless and even disastrous in safety-critical applications. Rigorously accounting for uncertainties in process engineering models is particularly challenging due to their nonlinear and combinatorial nature. The goal of my research group will be to develop scalable solutions to optimization and control problems under uncertainty that possess theoretical performance guarantees. In particular, our focus will revolve around the following broad research themes.

Optimization and control of dynamic systems under uncertainty: There are several applications of this model class in process engineering, including bioprocess optimization under parametric and implementation-related uncertainties, optimal experimental design for inferring parameters in constrained dynamic systems, and model predictive control of dynamic systems subject to stochastic disturbances. Existing approaches typically work with an explicit discretization of the dynamic system, which may lead to inaccurate solutions and increased computation times. Practical optimization approaches usually do not provide rigorous optimality guarantees as well. Our goal will be to develop efficient and implementable optimization schemes that leverage state-of-the-art methods for simulating dynamic systems while simultaneously providing theoretical performance guarantees. In particular, we will consider optimization problems with embedded dynamic systems and chance-constraints/robust constraints to ensure reliable system operation, and develop local optimization methods and decomposition algorithms for solving these problems.

Modeling and optimizing the resilience of systems: A resilient system is one that can anticipate and prepare for changing conditions, and withstand and recover rapidly from disruptive events. Increasing uncertainty surrounding high-impact rare events such as climate-related disruptions and the ever-growing threat of cyberattacks has led to renewed interest in modeling and optimizing the resilience of critical infrastructure systems such as the electric power grid. Another application that has witnessed a recent surge in interest is optimization of the resilience of chemical plants to disruptive events. Although there isn’t a single agreed upon resilience metric for such systems, the associated models typically include several challenging features from the viewpoint of optimization, including discrete decisions to model resilience-enhancing alternatives, multiple objectives corresponding to different stakeholders, different models of uncertain constraints (such as probabilistic and robust constraints), and multi-stage and multi-level optimization frameworks. We will develop application-specific resilience metrics based on existing literature and by working with domain experts, and design decomposition approaches for tackling the resulting large-scale stochastic optimization models.

Sustainable process design and operation: The problem of sustainable design and operation of engineering processes involves several challenges including multiple economic and environmental objectives, multiple time-scales and multi-level modeling frameworks, the lack of clearly defined system boundaries, and uncertainty in and unavailability of model data. We will consider a multi-objective stochastic optimization model for sustainable design and operation of specific chemical processes under probabilistic constraints on the environmental objectives. Tailored decomposition approaches will be developed to solve the resulting large-scale stochastic optimization model.

Summary of past research:

Doctoral research: I developed a decomposition algorithm for solving a broad class of two-stage stochastic mixed-integer nonlinear programs, and implemented it in a general-purpose software for solving this class of problems. The software, which also includes implementations of other state-of-the-art algorithms, consists of about 100,000 lines of C++ code, and also includes a test library that has been used by other members of the process systems engineering community. I also investigated the rate of convergence of deterministic branch-and-bound algorithms for constrained optimization, and used this theory to understand when branch-and-bound algorithms can mitigate the undesirable cluster problem in constrained global optimization.

Postdoctoral research: I designed a local optimization algorithm for solving chance-constrained nonlinear programs that uses techniques from the machine learning community. I have also been working on investigating the theory behind a purely data-driven stochastic optimization approach, designing a local optimization method for solving a broad class of stochastic optimization problems, constructing better optimal power flow models in the face of renewable energy uncertainty and designing approaches to solve these models, and exploring the design of resilience metrics for the power grid.

Teaching Interests:

I am passionate about teaching, and have actively sought out teaching opportunities. During my undergraduate studies, I worked as a Mathematics Olympiad trainer at an academy in India for groups of twenty students. One trainee was among the forty students nationwide selected to attend the International Mathematics Olympiad Training Camp in 2010. At MIT, I was a teaching assistant for the graduate Chemical Reactor Engineering course for which I helped develop computational exercises. I am also passionate about creating freely accessible educational resources and disseminating them to disadvantaged students. At IIT Madras, I was a volunteer for the Science Activities team of the National Services Scheme where I designed and demonstrated science experiments in underprivileged schools. While at MIT, I also recorded video lectures on discrete math as part of a team that generated free online content for the entrance exam for the Indian Institutes of Technology. Our effort was supported by the MIT Office of Digital Learning, and a couple of my video lectures were featured on MIT OpenCourseWare.

My main teaching objective will be to instill critical-thinking and problem-solving skills in students. My teaching philosophy is to use lots of carefully-designed working examples to build intuition, to have clearly-specified learning objectives for each class and to continually assess students’ proficiency with respect to these objectives through in-class exercises, and to develop assignments and projects by drawing on applications in other chemical engineering subdisciplines (e.g., an exercise on sparse computational linear algebra based on sensitivity analysis of a concrete large-scale kinetic model).

I am particularly interested in teaching undergraduate and graduate-level courses on numerical analysis, optimization, control, and systems engineering. I am also interested in teaching advanced graduate-level courses on nonconvex optimization and stochastic optimization.

Selected Publications:

Dissertation (2018): Algorithms, analysis and software for the global optimization of two-stage stochastic programs, Massachusetts Institute of Technology (includes two working papers).

Kannan and P. I. Barton (2018). Convergence-order analysis of branch-and-bound algorithms for constrained problems. Journal of Global Optimization, 71(4), pp. 753-813.

Kannan and P. I. Barton (2017). The cluster problem in constrained global optimization. Journal of Global Optimization, 69(3), pp. 629-676.

Kannan and A. K. Tangirala (2014). Correntropy-based partial directed coherence for testing multivariate Granger causality in nonlinear processes. Physical Review E, 89(6), 062144.

Selected Working Papers:

Kannan, L. Roald, and J. Luedtke. Stochastic DC Optimal Power Flow With Reserve Saturation.

Kannan and J. Luedtke. A stochastic approximation method for chance-constrained nonlinear programs. Preprint at https://arxiv.org/abs/1812.07066

Kannan and P. I. Barton. GOSSIP: decomposition software for the Global Optimization of nonconvex two-Stage Stochastic mixed-Integer nonlinear Programs.

Kannan and P. I. Barton. A modified Lagrangian relaxation algorithm for two-stage stochastic mixed-integer nonlinear programs.

Selected Honors:

George M. Keller Graduate Fellowship, Dept. of Chemical Engineering, MIT, 2012.

Oil and Natural Gas Corporation Scholarship, India, 2012.

Reliance Heat Transfer Pvt. Ltd. Award for academic excellence, IIT Madras, 2012.

Institute Merit Award, IIT Madras, 2010 and 2011.