Research

My research focuses on developing mathematically grounded machine learning methodologies for computational science. I aim to transform machine learning from a black-box approximation tool into a reliable computational framework for solving, discovering, and understanding complex physical systems.

By integrating numerical analysis, mathematical structure, and physical principles directly into learning algorithms, I develop AI methodologies that are not only accurate but also reliable, scalable, and scientifically interpretable. My research spans scientific machine learning, data-driven physics discovery, uncertainty quantification, and digital twins for engineering applications.

1. Scientific Machine Learning and Computational Science

I focus on developing machine learning methodologies and numerical algorithms for computational science, with particular emphasis on partial differential equations and scientific computing. My long-term objective is to establish scientific machine learning as a rigorous computational methodology that complements traditional numerical simulation while enabling efficient prediction, simulation, and scientific discovery.

A central theme of my research is the integration of mathematical analysis with machine learning. I develop physically and mathematically consistent learning algorithms by preserving intrinsic structures arising from governing equations, including hyperbolicity, conservation laws, entropy structure, stability, and boundary conditions.

Another major research direction is the development of machine learning methods for discovering governing equations, constitutive relations, and closure models directly from simulation and experimental data.

Research Topics

• Scientific Machine Learning
• Machine Learning for Partial Differential Equations
• Operator Learning
• Reduced-Order Modeling
• Multi-Fidelity Modeling
• Data-Driven Physics Discovery
• Numerical Analysis
• Structure-Preserving Algorithms

2. Uncertainty Quantification and Digital Twins

I develop uncertainty-aware computational methodologies for reliable prediction and decision making under limited or noisy observations. My research integrates Bayesian inference, probabilistic modeling, and active learning to quantify predictive uncertainty and efficiently combine simulation with observational data.

These methodologies provide the computational foundation for reliable digital twins and uncertainty-aware engineering analysis.

Research Topics

• Uncertainty Quantification
• Bayesian Inference
• Active Learning
• Data Assimilation
• Inverse Problems
• Digital Twins

3. Collaborative Research in Computational Engineering and Physical Sciences

I actively collaborate with researchers across computational engineering, applied mathematics, and physical sciences to develop and validate machine learning methodologies for challenging multiscale and multidisciplinary problems. These collaborations enable fundamental methodologies to be translated into practical computational tools for complex engineering systems.

Transcritical and Supercritical Fluid Modeling (Purdue University)

In collaboration with the School of Aeronautics and Astronautics, Purdue University, I develop machine learning and computational methods for transcritical and supercritical fluid systems. Representative research topics include thermodynamic modeling, transport phenomena, molecular dynamics, phase equilibrium, and high-pressure fluid mechanics.

Radiation Transport and Plasma Modeling (University of Notre Dame)

In collaboration with the Department of Physics and the Department of Aerospace and Mechanical Engineering, University of Notre Dame, I develop structure-preserving machine learning methods and numerical algorithms for radiation transport and plasma modeling. Current research includes hyperbolic systems, moment methods, neural closure modeling, discontinuous Galerkin methods, and data-driven constitutive modeling.

Molecular Simulation and Transport (Purdue University)

In collaboration with the School of Aeronautics and Astronautics, Purdue University, I develop machine learning methodologies for molecular simulations and transport phenomena. Representative applications include evaporation, vapor–liquid equilibrium, mass transport, and surrogate modeling based on molecular dynamics simulations.

Computational Mechanics and Digital Twins (Purdue University)

In collaboration with the School of Aeronautics and Astronautics, Purdue University, I develop reduced-order modeling techniques, uncertainty-aware computational methods, and digital twin technologies for computational mechanics. Representative applications include parameterized structural systems, scientific machine learning, and data-driven digital twins for engineering analysis.