Geometry and Dynamical Systems in Machine Learning and Control - Thesis by Victor D. Dorobantu

Aug 5, 2026

Upload by Finn

For many problems in machine learning and control, rich information about underlying geometry and dynamics can be leveraged to build robust, performant solutions through new algorithms, optimizations, and designs. This thesis examines four problem settings that test this assumption. It covers conformal generative modeling via computational geometry for 2D surface simplification and registration, flow-based models as plug-and-play subroutines, data-driven robust optimization with convex geometry for dynamics uncertainty in control, and compactly-restrictable policy optimization with constrained policy search.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages131

Reading Time5 h 30 min

AccessFree to download

Acknowledgements

Abstract

Geometric information for machine learning and control

Conformal generative modeling

Data-driven robust optimization in control

Compactly-restrictable policy optimization

Geometry and Dynamical Systems in Machine Learning and Control Thesis by Victor D. Dorobantu In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2023 Defended May 25, 2023 ii © 2023 Victor D. Dorobantu ORCID: 0000-0002-2797-7802 All rights reserved iii ACKNOWLEDGEMENTS Like some instances of describing a set via a description of its complement, it might be easier for me to describe all the people who haven’t helped make this thesis a reality than to describe all the people who have. Nevertheless, I’ll attempt the latter. Thank you to the Computing and Mathematical Sciences department at Caltech, for trusting me educating me, connecting me with all sorts of brilliant people, and for pointing me in the direction of applied math. I can’t believe all the things I know now, especially all the things that 2017 me never thought I would learn. Thankyou to Venkat Chandrasekaran and Andrew Stuart for spearheading my dive into applied math. Thank you to Walter Kortschak, Adam Wierman, and Chris Umans for the generous support and flexibility you afforded me to pursue what inspired me. Thank you to Riley Murray and Natalie Bernat for your advocacy and for making me (and my whole class) feel welcome. A very broad thank you to the Yue Crew1 and my unofficial, adoptive AMBER Lab. It was a joy to get to know all of you as researchers and as people. Your voracious appetites to learn, thought provoking conversations, and affinity to laughs will be the most memorable parts of my experience here. Thank you to Hoang Le for being my mentor early on, and thank you to Charlotte Borcherds for putting up with my half-baked ideas and pushing our work forward nonetheless. Thank you to Ryan Cosner for jumping head-first into the weird world of sampled-data control and helping us all find our ways. Thank you to Sarah Dean for such smooth remote collaboration, and to Jason Choi, Fernando Castañeda, and Bike Zhang for the years of chatting and learning. Thank you to Yousuf Soliman and Peter Schröder for the truly absurd amount of geometric insights you offered. Research can have a very high activation energy and you two were so often the catalysts. Thank you to Ivan Dario Jimenez Rodriguez and Albert Li for all the fantastic ideas and the nerd snipes. My perspectiveson geometry, generative modeling, and robotic manipulation would be woefully insufficient without all of our conversations. I wouldn’t understand geometry the way that I do without the many, many whiteboard sessions with Noel CsomayShanklin; thank you for always agreeing to study everything just for the fun of it, but also for knowing how to turn what we learned into actual research. Thank you 1I am still a little disappointed that that is not the official name. iv to Kamyar Azizzadenesheli for helping me find the math I love in my work and for always being willing to dive into the details. Thank you to John Dabiri for agreeing to come along my whirlwind of a research journey at some of its most critical stages. Thank you to Keenan Crane and Steve Brunton for teaching me almost everything I know about differential geometry and partial differential equations, respectively. Perhaps most impressively, you taught me all ofthis without even knowing you were teaching me; thank you for all of the time and effort you put into your videos. Thank you to Kristján Eldjárn Hjörleifsson for all the Kitchen Companionship and all the Turtle Time. All the extra time I had with you here was a delight. You changed the way I see and understand the world for the better. I hope we both continue deep living and deep learning. Also, while I’m at it, thank you to the Caltech Turtles. Thank you to Andrew Taylor for just about everything in my experience here. Thank you for understanding analysis with me, teaching me most of what I know about nonlinear control, and bringing me along a wild arc of

FAQs

What central assumption does the thesis investigate?

It tests the assumption that rich information about underlying geometry and dynamics can be leveraged to create robust, high-performing solutions in machine learning and control.

How does the thesis approach conformal generative modeling?

It uses computational geometry techniques to simplify and register complex 2D surfaces, enabling flow-based generative models as plug-and-play subroutines.

What role does geometry play in robust optimization for control?

The thesis models the impact of dynamics uncertainty across several control frameworks using convex geometry to support data-driven robust optimization.

Aug 5, 2026

Upload by Finn