(2gb) Inverse Design of Complex Flow Systems Using Theory and Differentiable Direct Numerical Simulations

My research aims to develop computational approaches that will help us realize the vision of application-based tailored flow behavior of complex fluids.

The initial research directions will be to advance the area of differentiable programming to solve inverse transport problems, develop accurate and end-to-end differentiable models of complex fluids that naturally integrates experimental data and the state-of-art in our understanding of such systems, and apply these techniques to further our understanding of suspension properties-rheological response relationship.

Direction 1: Differentiable programming is a powerful technique that allows us to perform gradient-based optimization on functions that are not traditionally differentiable. This technique is the key driver in the machine learning community and has many potential applications in solving inverse problems, particularly in the area of fluid mechanics . An example of using differentiable programming in colloidal systems could be to tailor the properties of a polydisperse suspension to yield a particular rheological response under certain flow conditions. To achieve this, we need to develop differentiable numerical techniques to solve the transport equations of such systems.

Direction 2: The second direction of my proposed research program is to develop novel models that relate the properties of the suspension system to the rheological response which naturally integrates experimental data and our physical understanding. By building end-to-end differentiable direct numerical simulations of complex fluids, one can systematically iterates over the whole solution trajectory to improve the accuracy of the predicted flow behavior when compared to the experiment.

Direction 3: The third objective of my research is to apply the developed models to tailor the flow behavior of complex fluids for industrially inspired applications.

Teaching Statement

As an educator, I am passionate about creating an interactive classroom environment that stimulates students' engagement with the subject matter. In the courses I feel well equipped to teach which include fluid mechanics, mathematical numerical methods, statistical mechanics, and transport phenomena, I strive to provide my students with hands-on activities and simulations that allow them to explore the material in a more interactive way. I am a believer in the use of real-time simulation tools which enable students to engage with the material in a more dynamic way. For example, in the fluid mechanics course, I might create interactive simulations using tools like Jupyter notebook that allow students to experiment with different flow parameters. By creating visual representations of abstract equations and concepts, students can develop a better understanding of the material and gain a deeper appreciation for the power and limitations of numerical methods.

In addition to the core courses, I aim to develop two new courses. The aim of the first course is to acquaint undergraduate/graduate students with the application of differentiable programming to solve fundamental and industrially related problems in physical sciences such as fluid flow and programming the material self-assembly. The second course will focus on analyzing breakthrough papers in the field of fluid mechanics to help students understand the thinking process brilliant scientists go through to define a problem and the way to approach it. This course will target graduate students.