About Me

I am a fourth year Mechanical and Aerospace Engineering PhD student at UC San Diego, working under Prof. Boris Kramer. I have been working on efficient, scalable numerical methods for implementing nonlinear balanced truncation model reduction. Through that, my research broadened to the more general problem of scalable numerical methods for solving Hamilton-Jacobi-Bellman Partial Differential Equations, which naturally arise in nonlinear control theory. The success of linear control theory and linear model reduction stems directly from the availability of efficient, easy-to-use solvers; our goal is to develop these types of tools for nonlinear systems, since nonlinear, high-dimensional dynamical systems which are ubiquitous throughout science and engineering. My current work on Kronecker product-based numerical methods for nonlinear balancing and nonlinear optimal control for high-dimensional systems can be found here on my GitHub!

My background is in Engineering Mechanics, which I studied during my BS and MS degrees at Virginia Tech. During this time, I was exposed to a variety of problems, ranging from curiosity-driven science to aerospace-application driven problems, such as through my design teams and my internship at Pratt and Whitney. Furthermore, my master’s work focused on vibration testing, specifically for railroad applications. Through all of these experiences, I was exposed to the need for general methods for efficiently simulating and analyzing complex engineering systems with features such as nonlinearity and complex geometry. This has motivated me to shift slightly towards the applied mathematics side of engineering to study model reduction methods during my PhD, which brought me to UCSD to work with Prof. Boris Kramer.

News

August 2024: Our paper titled “Computing Solutions to the Polynomial-Polynomial-Regulator Problem” was accepted to CDC 2024. I am excited to visit Milan in December 2024 and look forward to presenting this recent work.

July 2024: I presented my work on computations for nonlinear balancing for polynomial drift systems at ACC 2024 in Toronto. This work, along with the work I presented at SIAM CT last summer, allows us to compute nonlinear balancing energy functions for general control-affine nonlinear systems of arbitrary polynomial degree. All of this work will be published in an upcoming journal paper that is currently in the review stages.

March 2024: Our paper titled “Scalable Computation of H-Infinity Energy Functions for Polynomial Drift Nonlinear Systems” was accepted for ACC 2024. I am excited to visit Toronto and present this work in July! I also just submitted a paper titled “Computing Solutions to the Polynomial-Polynomial-Regulator Problem” to CDC 2024; this represents an exciting connection between our model reduction work and a more general optimal control problem. I hope to present this in Milan in December!

February 2024: My advisor Prof. Boris Kramer is organizing this year’s Model Reduction and Surrogate Modeling (MORe) conference here in San Diego this September 9-13, 2024. I just submitted an abstract, and I look forward to having our wonderful research community here to visit later this year to share all of the exciting research developments!

October 2023: Happy first birthday to my wonderful crazy little dog.

August 2023: I am planning to attend ACC 2024 in Toronto next year to present more of my work on computations for nonlinear balancing; I will present a generalization of my work to compute energy function approximations for systems with polynomial drift dynamics. I will also be visiting Blacksburg again in December 2023!

July 2023: I presented my work on computations for nonlinear balancing for polynomial input systems at the SIAM Conference on Control and Its Applications in Philadelphia.

May 2023: Had a great time at the Nonlinear Model Reduction for Control workshop at Virginia Tech presenting my work on computations for nonlinear balancing for polynomial input systems. It was great to have our community together in Blacksburg!

January 2023: Happy New Year! This year I’m excited to be attending the Nonlinear Model Reduction for Control workshop at Virginia Tech May 22-26th, and I also hope to attend the SIAM Conference on Control and Its Applications in Philadelphia in July.

June 2022: I survived the first year of my PhD program! I took some wonderful control theory classes which UCSD’s mechanical engineering department has to offer, along with some really stimulating math classes the department offers such as real and functional analysis. I also passed my Department Qualifying Exam (DQE). Many thanks to my advisor Prof. Boris Kramer and my committee members Prof. Patricia Hidalgo-Gonzalez and Prof. Jorge Cortes. In the coming weeks, I will be taking a small vacation to Italy to visit family and recover from a challenging year of courses.

March 2022: I just returned from attending the 2022 Spring School on Theory and Applications of Port-Hamiltonian Systems at the beautiful island of Fraueninsel (Chiemsee), Germany. It was a wonderful opportunity to learn about port-Hamiltonian systems, and I met a lot of wonderful colleagues whom I hope to see again in the near future!

January 2022: I’ve been accepted to the 2022 Spring School on Theory and Applications of Port-Hamiltonian Systems, which I am excited to attend. The workshop will take place March 20-25 in Fraueninsel (Chiemsee), Germany (pictured below).

September 2021: I’ve moved from Virginia Tech to San Diego to pursue a PhD in Mechanical and Aerospace Engineering at UCSD with Prof. Boris Kramer.

July 2021: I completed my master’s thesis defense! Many thanks to my advisor Prof. Pablo Tarazaga and my committee members Prof. Shane Ross and Prof. John Domann.

February 2020: I will be giving a talk at the 38th International Modal Analysis Conference, in Houston, Texas. In my presentation, I will share some results from finite element simulations I have been using to study low-frequency wave propagation in rails for measuring stress non-destructively.

February 2019: I will be giving a talk at the 90th Shock and Vibrations Exchange, in Atlanta, Georgia. In my presentation, I will share a new method which Kameron Mize, Dr. tarazaga, and I have worked on to facilitate projection-based component vibration testing.