Current Research Projects

Fluid flow that extrudes through a shaped nozzle can exhibit a different cross-sectional shape than the nozzle itself due to fluid-structure and fluid-fluid interactions after transiting the orifice. These effects have contributed to long-standing problems in manufacturing, particularly in glass/fiber drawing, additive manufacturing, and microparticle fabrication. Currently, designing extrusion flow requires experiments and/or numerical simulations to determine the extruded fluid flow shape for a given nozzle. Designing nozzle geometry and flow conditions for a desired extrusion flow shape (the inverse problem) then requires trial-and-error experiments or a computationally expensive many-query iterative search. The goal of this work is to create an end-to-end framework enabling rapid prediction of extrusion flow shapes (fast forward models) and efficient design of nozzles/flow conditions (solving the inverse problem).

Bayesian inference has recently been used with machine learning (specifically, Generative Adversarial Networks, or GANs) to solve ill-posed inverse problems while quantifying uncertainty in the result, even when the observed parameters have incomplete or missing information. This prompts a more challenging type of inverse problem: can interior material properties be determined using only measurements taken only along a domain's boundary? Solving this type of surface-based tomography problem while quantifying uncertainty would be useful for soft tissue analysis within medical science, e.g., identifying breast cancer using tissue displacement measurements. The short-term goal of this project is to use simple finite element models to determine how well Bayesian inference can work as an inverse problem solver and quantify uncertainty for 2D and 3D domains, while the long-term goal is to apply the method to real-world breast cancer patient measurements.