Ruchi Sandilya, Ph.D.
Welcome to my website! I am an applied mathematician with background in control theory for complex dynamical systems. Presently, I am bringing these concepts together with machine learning to address the challenges associated with the diagnosis and treatment of major depressive disorder.
Selected Research Projects
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Major depression is a common disorder with high rates of treatment resistance. In this project, my goal is to bring the ideas of control theory and machine learning for the development of personalized closed-loop therapy for treatment-resistant depression.
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The Boussinesq system is frequently used to model non-isothermal complex fluid flows. In this project, I worked on developing efficient feedback control laws to stabilize the Boussinesq system. I contributed towards developing software in Python using FEniCs, a finite element library, to solve the control system. Our method optimizes energy use in the aircraft or a building by controlling the indoor environment such as temperature, humidity, and air quality. The design of such energy-saving buildings is essential to meet national energy and environmental challenges. It is critical to reduce energy consumption and associated greenhouse gas emissions that contribute to global warming. Modeling and controlling the air quality of the indoor environment has gained more importance recently due to the ongoing COVID-19 pandemic and will remain in focus due to the possibility of another epidemic in the future and higher hygienic standards in the post-covid era.
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Our goal is to design novel techniques for control and feedback stabilization of unstable complex fluid models with uncertain parameters using neural networks (NN) with a Bayesian approach. We use the linearized system around an unstable stationary solution to construct NN-based feedback law to achieve stabilization of the nonlinear system. We are performing systematic numerical experiments to illustrate the efficacy of our algorithms. The software is being developed in python using PyTorch and other machine learning libraries.
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My graduate research contributions were focused on developing efficient solution techniques for difficult optimal control problems governed by partial differential equations (PDEs). These equations represent mathematical models for many real-life applications including laser thermotherapy for cancer treatment, modeling of drug kinetics, modeling of complex brain dynamics, modeling and simulation for optimization of in vitro tissue growth environments in tissue engineering, optimal shape design of an aircraft, and enhanced oil recovery in petroleum engineering. I derived the optimal convergence estimates of the finite element schemes and verified the accuracy and efficiency of the method by conducting several numerical tests in MATLAB. In view of applications to engineering and biology, I extended the theory and practice of controls to the oil recovery techniques based on the injection of immiscible fluids in the reservoirs to extract hydrocarbons from the earth’s subsurface and linear poroelasticity equations that can be used to model blood flows through the beating myocardium.