About Me
I am a Professor and Chair of the Department of Mathematics at Clarkson University. My research lies at the intersection of computational mathematics, scientific computing, optimization, and data science.
My current interests include numerical methods for partial differential equations, meshfree and radial basis function methods, power system modeling and simulation, machine learning, and physics-informed neural networks. I am particularly interested in developing efficient computational algorithms for solving complex problems arising in engineering, energy systems, and scientific applications.
In addition to research, I enjoy teaching a broad range of courses in mathematics, data science, and computational methods, and mentoring undergraduate and graduate students in interdisciplinary research projects.
Google Scholar PublicationsCourses Taught
Education
- Ph.D., Computational Science (Mathematics), University of Southern Mississippi, 2010. Dissertation: Localized Radial Basis Function Method for Solving Partial Differential Equations.
- M.S., Mathematics, Harbin Normal University, 2006. Thesis: The Homotopy Method for Multi-objective Programming Problems.
- B.S., Mathematics and Applied Mathematics, Harbin Normal University, 2003.
Professional Experience
Clarkson University, Potsdam, New York, USA
| July 2025 - Present | Professor, Department of Mathematics |
| July 2024 - June 2026 | Chair, Department of Mathematics |
| August 2019 - June 2024 | Executive Officer, Department of Mathematics |
| February 2018 - June 2025 | Associate Professor, Department of Mathematics |
| July 2012 - February 2018 | Assistant Professor, Department of Mathematics |
Centre de Recherches Mathématiques (CRM), Montréal, Canada
| March 2019 - August 2019 | Simons Scholar and Visiting Research Professor |
Rowan University, Glassboro, New Jersey, USA
| September 2011 - June 2012 | Assistant Professor, Department of Mathematics |
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA
| August 2010 - August 2011 | Research Associate, Department of Electrical Engineering and Computer Science |
IMPOL Aluminium Industry, Slovenska Bistrica, Slovenia
| September 2009 - February 2010 | Research Associate |
Harbin University, Harbin, China
| June 2006 - January 2007 | Instructor, Department of Mathematics |
Harbin Normal University, Harbin, China
| September 2005 - January 2006 | Instructor, Department of Mathematics |
Research Interests
Numerical PDEs
Numerical methods for ordinary and partial differential equations, including collocation, meshfree methods, and boundary value problems.
Meshfree & RBF Methods
Radial basis functions, localized radial basis function methods, and numerical algorithms for complex geometries.
Optimization
Homotopy continuation, constrained nonlinear optimization, multiobjective optimization, and computational algorithms.
Scientific Machine Learning
Machine learning, physics-informed neural networks, and data-driven methods for solving PDEs and modeling complex systems.
Power Systems
Power system modeling and simulation, resource adequacy, reliability analysis, and fast Monte Carlo simulation methods.
Data Science & Statistics Learning
Data science education, statistical learning, regression, classification, computational tools, and applications.
Keywords
- Radial Basis Functions
- Meshfree Methods
- Partial Differential Equations
- High Performance Computing
- Stochastic Differential Equations
- Physics-Informed Neural Networks
- Power System Reliability
- Data Science
Publications
My research has resulted in publications in numerical analysis, scientific computing, optimization, machine learning, power systems, and applied mathematics. For a complete and up-to-date publication list, please visit my Google Scholar profile.
Research Projects and Collaborations
Current Research Projects
- Power System Reliability and Resource Adequacy: Fast Monte Carlo simulation, sequential Monte Carlo methods, replicated Monte Carlo methods, optimization-guided reliability analysis, and uncertainty quantification for modern power systems.
- Scientific Machine Learning and Physics-Informed Neural Networks: Data-driven and physics-informed computational methods for solving ordinary and partial differential equations.
- Meshfree and Radial Basis Function Methods: Development and analysis of meshfree numerical methods, scattered data interpolation techniques, and localized radial basis function methods for high-dimensional differential equations.
- Homotopy Methods for Optimization: Homotopy continuation methods for nonlinear systems, constrained optimization, multiobjective optimization, and optimal power flow problems.
- Data Science and Statistical Learning: Statistical modeling, machine learning, computational data analysis, and interdisciplinary applications.
Selected Research Collaborations
- Climate Change and Zoonotic Spillover Modeling: Mathematical modeling and computational analysis of the impacts of climate change on disease transmission and zoonotic spillover.
- Cyber-Resilient Distributed Energy Resource Control: Interdisciplinary collaboration on smart grids, distributed energy resources, and power system security.
- Groundwater Remediation Modeling: Numerical simulation of groundwater flow and reactive media treatment systems in collaboration with environmental engineers.
- Image-Based Multi-scale Modeling of Calcium Signaling in Ventricular Cells, Department of Electrical Engineering and Computer Science, University of Wisconsin - Milwaukee (2010 - 2011).
- Computational Modeling of Hot-Tearing and Other Casting Defects, IMPOL Aluminum Industry, Slovenia (2009-2010).
Industrial and Interdisciplinary Collaborations
- Climate Change and Zoonotic Spillover Modeling: Mathematical modeling and computational analysis of the impacts of climate change on disease transmission and zoonotic spillover.
- Cyber-Resilient Distributed Energy Resource Control: Collaborative research on smart grids, distributed energy resources, cybersecurity, and power system resilience.
- Groundwater Remediation Modeling: Numerical simulation of groundwater flow, contaminant transport, and reactive media treatment systems in collaboration with environmental engineers.
- Image-Based Multi-scale Modeling of Calcium Signaling in Ventricular Cells: Collaborative research with the Department of Electrical Engineering and Computer Science, University of Wisconsin-Milwaukee (2010-2011).
- Computational Modeling of Hot-Tearing and Casting Defects: Collaborative research with IMPOL Aluminum Industry, Slovenia (2009-2010).
Research Areas
- Numerical PDEs
- Meshfree Methods
- Radial Basis Functions
- Optimization
- Scientific Computing
- Machine Learning
- Physics-Informed Neural Networks
- Power Systems
- Data Science
- Statistical Learning
Research Grants and Funded Projects
- NSF Grant 2325267 (2023-2026) - Senior Personnel, Enhancing Mathematical Models to Investigate the Influences of Climate Change on Zoonotic Spillover.
- NSA Grant H98230-22-1-0008 (2022-2023) - Principal Investigator, Research Experience for Undergraduates in Mathematics. Award Amount: $93,444. [Project Website]
- NSA Grant H98230-21-1-0336 (2021-2022) - Principal Investigator, Research Experience for Undergraduates in Mathematics. Award Amount: $41,344. [Project Website]
- NSF Grant 1431882 (2015-2019) - Co-Principal Investigator, COMPASS: Co-Ordinated Math Physics Assessment for Student Success. Award Amount: $545,722.
- Heilongjiang Provincial Natural Sciences Foundation (2007-2008) - Principal Investigator, New Algorithms for Nonlinear Optimization Problems.
- National Natural Science Foundation of China (2005-2007) - Principal Investigator, Optimality Conditions and Homotopy Methods for Multiobjective Optimization Problems.
Teaching
The following list combines courses from my previous teaching page with recent Clarkson teaching information. Older entries are preserved by semester and institution.
Courses Taught
Undergraduate and Graduate Courses
- MA131 - COMPASS Calculus I
- MA132 - COMPASS Calculus II
- MA180 - Introductory College Mathematics
- MA181 - Basic Calculus
- MA200 - Introduction to Mathematical Modeling and Software
- MA211 - Discrete Mathematics and Proof
- MA230 - Space and Projective Geometry
- MA231 - Calculus III
- MA232 - Elementary Differential Equations
- MA300 - Seminar in Actuarial Mathematics
- MA321 - Advanced Calculus I
- MA330 - Advanced Engineering Mathematics
- MA331 - Fourier Series and Boundary Value Problems
- MA332 - Intermediate Differential Equations
- MA339 - Applied Linear Algebra
- MA377 - Numerical Methods
- DS/MA239 - Linear Algebra for Data Science
- DS/MA241 - Intro to Data Science
- MA531 - Initial and Boundary Value Problems and Partial Differential Equations
- MA571 - Numerical Differential Equations
Courses Taught at Previous Institutions
- MATH 01.130 - Calculus I
- MATH 01.210 - Linear Algebra
- MATH 01.236 - Mathematics for Engineering Analysis II
- MATH 03.125 - Calculus Technologies and Applications
- Advanced Calculus
- Functional Analysis
Students and Mentoring
Current Ph.D. Students
-
Ibraheem Abiodun Yahayah (2023-Present)
- Dissertation: Working in progress
Visiting Scholars
-
Jing Niu (2018-2019)
- Currently Full Professor, Harbin Normal University
-
Liqun Ban (2013-2014)
- Currently Full Professor, Harbin University of Science and Technology
Graduated Ph.D. Students
- Dissertation: A Deterministic Homotopy Framework for Constrained Multi-Objective Optimization with Application to Optimal Power Flow Problem
- Dissertation: Localized Radial Basis Function Collocation Methods for Data Interpolation and Solving Partial Differential Equations
- Current Position: Lecturer, SUNY Canton
- Dissertation: Meshfree Methods Based on Radial Basis Functions for Solving Partial Differential Equations: From Strong Form to Weakened Weak Form
- Current Position: Assistant Professor, Fordham University
Professional Service and Recognition
Awards and Recognition
- Commendable Leadership Award, Clarkson University, 2026.
- Commendable Service Award, Clarkson University, 2026.
Faculty Service and Academic Affiliations
- Faculty Advisor for the Association for Women in Mathematics (AWM), Pi Mu Epsilon (PME), SIAM Student Chapter, Mathematics Club, and Society of Asian Scientists and Engineers (SASE).
- Affiliated Faculty, Institute for a Sustainable Environment, Clarkson University.
- Courtesy Appointment, Institute for STEM Education, Clarkson University.
Conference Organization and Outreach
- Mathematics Conference and Competition of Northern New York (MCCNNY) - Organizer and Host, Clarkson University
- A Mini-Conference on Applied Statistics and Computational Mathematics - Co-Organizer with Sumona Mondal, Clarkson University, October 2013.
- Faculty Seminar Series, Associated Colleges of the St. Lawrence Valley (2013-2014, 2018-2019, 2022-2023).
Contact
Guangming Yao
Professor and Chair, Department of Mathematics
Clarkson University
Email: gyao@clarkson.edu
Office: SC 361A
Phone: (315) 268-6496