Hyemin Gu

I am a postdoctoral researcher in Markos Katsoulakis’s group at UMass Amherst, where I completed my Ph.D. in Applied Mathematics with the dissertation Robust Generative Modeling with Wasserstein Proximal Regularization. My research places machine learning models on mathematical foundations, so that their behavior can be predicted, analyzed, and controlled through the underlying theory.

Research interests. Mathematically grounded machine learning; generative modeling; stable learning algorithms; dynamical systems; scientific applications of machine learning.

My work centers on

• formulating well-posed learning objectives for generative modeling and dynamical systems through optimal-transport, mean-field-game, and optimal-control principles;
• developing stable learning algorithms through regularizations such as Wasserstein-1 / Wasserstein-2 proximal and Lipschitz regularization; and
• translating these principles into scalable algorithms for scientific applications, including single-cell dynamics and supply-chain networks.

Under DARPA’s The Right Space program, I am developing principled machine learning architectures for complex learning and optimization, together with dynamical-system simulators for supply-chain networks. This includes stable residual neural architectures characterized through Hamilton–Jacobi and optimal-control formulations, and ISOMORPH, a Markov-chain-based digital twin of multi-echelon logistics networks for scalable simulation and forecasting benchmarks. In parallel, I lead the mathematical and algorithmic development of PROFET, a gradient-flow-based generative framework for continuous trajectory inference from sparse scRNA-seq data.

A recurring challenge in mathematical sciences is balancing abstraction, which enables transferability across domains, with concrete problem formulations, which often drive practical advances. My long-term goal is to let mathematical theory and real-world applications continuously inform and strengthen one another.