Mayank Baranwal

Reduction of Chemical Networks

This project aims at developing theory and algorithms for network inference in the physical sciences and engineering with particular emphasis on dynamical chemical and biological reaction networks. Hybrid methods using machine learning (black-box) and mechanistic state space modeling (white-box) are of special interest. The project involves developing sparse learning algorithms for discovering new principles for predicting network dynamics.

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Fixed-Time Distributed Optimization

We investigate the fixed-time distributed convex optimization problem for continuous time multi-agent systems under time-invariant topology. A novel type of nonlinear protocol coupled with tools from Lyapunov theory is proposed to minimize the sum of convex objective functions of each agent in fixed-time, i.e., convergence time is independent of initial conditions. Our algorithm is the first such protocol for achieving distributed optimization in fixed-time.

Determination of True Number of Clusters

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the clustering solutions with different number of clusters. We show that the datasets where natural clusters are a priori known, the clustering solutions that identify the natural clusters are most persistent - in this way, this notion can be used to identify solutions with true number of clusters.

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Combinatorial Optimization Problems

This project aims at extending mean-field based approach to several NP-hard problems, such as, data clustering, traveling salesman problem and its variants, image segmentation, mixed-integer linear programming, shape clustering, vehicle routing problems, graph clustering, minimum multiway k-cut, graph coloring and maximum independent set problems. The key idea is to lift the solution space to a space of probability distributions and employ maximum entropy principle to efficiently constrain the solutions. Below are some of the results of our approach to a variety of optimization problems.

Enabling the Grid of the Future

This project aims at developing innovative hardware and software solutions to integrate and coordinate generation, transmission, and end-use energy systems at various points on the electric grid. These control systems will enable real-time coordination between distributed generation, such as rooftop and community solar assets and bulk power generation, while proactively shaping electric load.

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Neural coding in barrel cortex

The project explores neural coding in the barrel cortex of head-fixed mice that tracks walls with their whiskers in tactile virtual reality. The goal is to obtain correlations among activities of different neuron units.