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More Manageable Models

PhD Students Work to Make Nonlinear Dynamical Systems Tractable

A nurse triaging chest pain patients in an intensive care unit needs to prioritize the people who are most likely to enter cardiac arrest. Unfortunately, accurately assessing that risk requires an intricate understanding of blood pressure, cholesterol levels, weight, dietary and exercise habits, and a myriad of other factors for each patient.

But what if, instead, the assessment was a simple model that the nurse could plug three of the patient’s readings into?

Assistant Professor Dan Wilson researches how to reliably reduce the dimensionality of models to better understand nonlinear dynamical systems, like the factors leading to arrhythmia, cardiac arrest, and neurological disorders like Parkinson’s disease.

As doctoral students in Wilson’s lab, Adharaa Dewanjee and Talha Ahmed are helping push the boundaries of model reduction and system analysis.

What sparked your interest in this field?

Dewanjee: My background is in electrical engineering and computer science, but I have always been interested in biomedical issues. Computational neuroscience allows me to apply my computational expertise to neuroscience applications.

Ahmed: I have always been fascinated with biological phenomena. In computational neuroscience, we mimic and study the brain and its associated functions through a mathematical lens to gain a better understanding of its innate workings—so engineers like me can understand biology better by applying the techniques we already have.

Why is it valuable to simplify models of nonlinear dynamical systems?

Dewanjee: The majority of real-life systems are highly complex and multidimensional, making it difficult to control, model, and analyze them. Reducing the dimension of the model for a nonlinear dynamical system facilitates the system’s analysis.

Ahmed: Reducing and simplifying nonlinear dynamical models results in a much more tractable, computationally efficient approximation of the full model’s dynamics. Modelling and predicting the states of such systems allows us to approximate their underlying behavior, analyze them, and foresee outcomes that might either be beneficial or detrimental to the system.

Why did you decide to pursue your doctoral degree at UT?

Dewanjee: I found Dr. Wilson’s research to be really intriguing and consistent with my prior research experience. Once I investigated the university more, I discovered that UT offers a wide range of individual development opportunities, both during coursework and in extracurricular activities like multicultural events, which made it the ideal graduate program for me.

Ahmed: Dr. Wilson’s research provides me the perfect opportunity to use model reduction techniques to make linear and nonlinear control theory techniques applicable to various biological models. UT is also one of the best public engineering schools in the US, with world-renowned faculty, a vibrant student community, and state-of-the-art facilities for research.

What impact do you hope your research will have?

Dewanjee: Reducing the dimension of systems is a crucial consideration in many real-world applications. I believe my research will help other engineers analyze and control any type of intricate, high-dimensional system more quickly and effectively.

Ahmed: For the last few years, I have been developing new data-driven model reduction techniques using neural networks. I hope that these strategies will introduce robust and configurable data-driven model reduction techniques that can help us deal with observable data more efficiently than we can with traditional methods.


Izzie Gall (865-974-7203,