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 (TRAGOS) 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.

Barbara Oakley, in her book A Mind for Numbers, highlights a common challenge in both mathematics and applied fields:

The challenge is that it’s often easier to pick up on a mathematical idea if it is applied directly to a concrete problem – even though that can make it more difficult to transfer the mathematical idea to new areas later. Unsurprisingly, there ends up being a constant tussle between concrete and abstract approaches to learning mathematics. Mathematicians try to hold the high ground by stepping back to make sure that abstract approaches are central to the learning process. In contrast, engineering, business, and many other professions all naturally gravitate toward math that focuses on their specific areas to help build student engagement and avoid the complaint of “When am I ever going to use this?”

My longer-term goal is to narrow this gap by letting insights from mathematical theory and applied problems continuously reshape one another.