Huan Lei

My research focuses on computational mathematics, particularly on developing numerical methods for learning partial differential equation (PDE) and stochastic differential equation (SDE) models arising from multi-scale problems. I am interested in designing structure-preserving algorithms that retain essential mathematical properties, such as conservation laws, variational structures, and physical constraints. A central aspect of my work is integrating scientific machine learning (SciML) with numerical analysis to construct accurate and physically interpretable PDE and SDE models of multi-scale systems directly from first-principle descriptions, where conventional approaches often show limitations.



Research Interests
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+ Multi-scale modeling
+ Structure-preserving PDE models and numerical schemes
+ Model reduction and stochastic simulations
+ Scientific machine-learning

###Education
Ph. D. 2012, Applied Mathematics, Brown University - Advisor:  George Karniadakis
B.S. 2005, Special Class for the Gifted Young, Univ. of Science & Technology of China

###Professional Appointment
Post-doctoral Associate, Brown University (2012 -2013)
Post-doctoral Associate, Pacific Northwest National Laboratory (2013 -2015)
Scientist, Pacific Northwest National Laboratory (2015 -2019)


###Openings
One Ph.D. position is available starting in Fall 2025 or Spring 2026. While my research is motivated by computational modeling of multi-scale problems, such as molecular, fluid, and kinetic systems, my primary goal is to develop mathematically rigorous and computationally efficient methods for learning and simulating complex dynamical systems. I seek motivated Ph.D. students with a strong background in numerical analysis, applied mathematics, or scientific computing who are interested in developing new numerical methods rather than applying existing techniques to domain-specific applications. If you are interested, please contact me by email.