HotCSE Seminar: Sebastián Gutiérrez Hernández

Name: CSE Ph.D. Student Sebastián Gutiérrez Hernández

Date: Wednesday, Nov. 12, 2025, at 12:00 p.m.

Location: Coda 230 (Google Maps link)

Lunch provided!

Title: Parametric Density Path Optimization

Abstract: We introduce Parametric Density Path Optimization (PDPO), a novel method for computing action-minimizing paths between probability densities. The core idea is to represent the target probability path as the pushforward of a reference density through a parametric map, transforming the original infinite-dimensional optimization over densities to a finite-dimensional one over the parameters of the map. We derive a static formulation of the dynamic problem of action minimization and propose cubic spline interpolation of the path in parameter space to solve the static problem. Theoretically, we establish an error bound of the action under proper assumptions on the regularity of the parameter path. Empirically, we find that using 3–5 control points of the spline interpolation suffices to accurately resolve both multimodal and high-dimensional problems. We demonstrate that PDPO can flexibly accommodate a wide range of potential terms, including those modeling obstacles, mean-field interactions, stochastic control, and higher-order dynamics. Our method outperforms existing state-of-the-art approaches in benchmark tasks, demonstrating superior computational efficiency and solution quality.

Bio: Sebastián Gutiérrez Hernández is currently a fifth-year CSE Ph.D. student in the Mathematics department at Georgia Tech. His main advisor is Dr. Haomin Zhou and he is co-advised by Dr. Peng Chen. Sebastián holds a bachelor's degree in Physics and Mathematics from the National Polytechnic Institute of Mexico and a Master's Degree in Applied Mathematics from the Research Center in Mathematics (CIMAT).
Sebastián's research focuses on computational methods at the intersection of optimal transport theory and scientific machine learning. His primary interest is extending the Wasserstein parametric framework to optimal transport problems with Lagrangian costs. As a secondary research direction, Sebastián leverages operator learning techniques to efficiently solve PDE-constrained optimization problems under uncertainty.

Sebastián is serving as the President of the SIAM Student Chapter at Georgia Tech since Fall 2025. If you are interested in attending or presenting in the chapter seminar series, please reach out to him.

About HotCSE

HotCSE is an academic seminar series to bring Ph.D. students in Computational Science and Engineering together to discuss interesting topics. The topics consist of high-performance computing, machine learning, data analysis, simulation, computational sustainability, medical informatics, etc.

The talks have always been enjoyable and have ranged from quite informal to formal conference style talks. Either chalks or slides can be used to help people understand your talk. It is also a great forum to practice conference talks and bounce around new ideas.

Currently the talks are sponsored by the School of Computational Science and Engineering. The goal of CSE is slightly broader than that of these talks - we want to bring more people outside CSE to discuss their related work here.