We explore a generalization of the Schrodinger Bridge Problem (SBP), which steers a probability distribution with prior nonlinear dynamics from an initial to final state, building an optimal controller for a broad set of prior dynamics. Specifically, we design a numerical solver for a pair of PDEs describing the generalized problem. Our framework of the SBP has applications to physics, computer graphics, and computer vision, with prior works utilizing special cases of the PDEs for smooth shape interpolation, digital animation, generative modeling, and seismic exploration. Using our generalized solver for the aforementioned applications, we develop improvements to sample generation and interpolation.

I’m interested in dynamical system modeling and optimal transport, as well as their many applications across the sciences. In developing optimization techniques for generic systems, my SuperUROP will expose me to a variety of numerical and theoretical tools used for controls. I hope to synthesize my computational and communication skills to solve real-world problems in nonlinear system modeling.