Biography

I am a fifth year PhD student in the Department of Mathematics at Oregon State University and I am working under the guidance of Professor Malgorzata Peszynska. I started my PhD in Mathematics in March 2021 and became a PhD candidate in February 2025 after completing my oral preliminary exam. I also earned my Master of Science in Mathematics from OSU in December 2023. My primary research interests are in applied and computational mathematics with a focus on numerical analysis and mathematical modeling of multiphysics phenomena. I mainly work with finite volumes and use Matlab at an advanced level for coding purposes. Additionally, I also worked and had experience with R, Maple, SPSS, Python, C. My ongoing PhD research, “Modeling and Numerical Analysis in Cryosphere” focuses on modeling processes in cold regions and in the Arctic, which takes advantage of a lot of experimentally collected data. This research continues from work that began as my Master's capstone project. As a researcher, my future plans include a focus on involving to develop and simulate complex, efficient, large-scale computational models, particularly in thermal conduction and fluid interactions, which handle vast datasets and require high performance computing resources to solve effectively.

Academic Status

PhD Student - 5th

Research Area/Department

Applied Mathematics; Data Science; Machine Learning/AI; Mathematics

Major/Specialty

Applied and computational mathematics with a focus on numerical analysis and mathematical modeling of multiphysics phenomena.

Degrees Earned or in Progress

Ph.D. student in Mathematics (Oregon State University, March 2021 - present). Ph.D. candidate in Mathematics (after completion of oral preliminary exam) (Oregon State University, February 2025 - present). Master of Science in Mathematics (Oregon State University, December 2023). B.Sc (Honours) in Mathematics (University of Sri Jayewardenepura (USJ), Sri Lanka, January 2015 - December 2018).

Academic Preparation

MTH 621-623: PDEs I, II and III, MTH 627: Advanced PDEs, MTH 654: Finite Elements, MTH 659: Multiphysics; Computational Mathematics Foundations, MTH 659: Solving Nonlinear Coupled PDEs, MTH 659: Analysis and Approximation of Flow PDEs, MTH 551: Numerical solutions to PDEs, MTH 552: Numerical solution to ODEs, MTH 551: Numerical Linear Algebra, MTH 581: Applied ODEs, MTH 659: Computational Wave Propagation, MTH 659: Computational Harmonic Analysis, MTH 563-565: Probability I, II and III, ST 511: Methods of Data Analysis.

Research/Publications

Publications: 1. M. Peszynska, P. Mathangadeera, M. Phelps, F. Felsch and N. Unger-Schulz, ''Heat Conduction with Phase Change in Soils with Macro-pores, Snow, and Cryoconite. Part I: Unified Model Derivation and Examples'', SEMA journal, August 2025; DOI 10.1007/s40324-025-00400-z. arxiv link: https://arxiv.org/abs/2508.05916 2. M. Peszynska and P. Mathangadeera, "Comparison of Implicit Time Stepping to the Scheme with "Apparent Heat Capacity" for a Thermal Model of Permafrost with Surface Terrain Dependent Boundary Conditions", Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2. Lecture Notes in Computational Science and Engineering, vol 154, pp 252-261, Editors Adelia Sequeira, Ana Silvestre, Svilen Valtchev, and Joao Janela, 2025, ISBN 978-3-031-86168-0 (print), 978-3-031-86169-7 (eBook). Author accepted manuscript link: https://sites.science.oregonstate.edu/~mpesz/documents/publications/ENUMATH_PeszynskaMathangadeera.pdf Research/technical projects: 1. Modeling and Numerical Analysis in Cryosphere, (Ph.D. Project: Oregon State University, In progress). Major Professor: Prof. Malgorzata Peszynska. 2. Implementation of the permafrost model (P-MODEL), P0-P0 finite elements (developed using Matlab). Developers: Praveeni Mathangadeera, Malgorzata Peszynska. Used in ENUMATH, July 2025. 3. Structure-Preserving Scientific Computing and Machine Learning Summer School and Hackathon, University of Washington, Seattle, WA, 6/23 - 6/25 2025. Hackathon project: Developing physics-informed preconditioners for a Thermal Radiative Transfer model, Project leader: Terry Haut (LLNL). Github link: https://github.com/jpgallagher1/PIMS-GroupB.

Research/Academic Interests

My primary research interests are in applied and computational mathematics with a focus on numerical analysis and mathematical modeling of multiphysics phenomena. I am particularly interested in applications in climate science related to the cryosphere, such as thermal conduction and fluid flow in cold regions. I would also like to work with computational methods such as finite volume techniques and implement them in scientific computing environments. Additionally, I am interested in high performance computing and the simulation of large-scale, data-driven models that support the understanding of climate related processes.

Computational and Data Science Areas

Applied Mathematics; Climate and Global Dynamics; Fluid and Plasma Physics; Geology and Solid Earth Sciences; Other Earth and Environmental Sciences

Motivation

I am a fifth year PhD student in the Department of Mathematics at Oregon State University and I am working under the guidance of Professor Malgorzata Peszynska. I would like to apply to the NSF National AI Research Resource (NAIRR) pilot and the High Performance Software Foundation (HPSF) projects to get an opportunity to extend my knowledge in computational methods, high performance computing, and modern data science tools that support advanced research in applied mathematics and multiphysics modeling. My primary research interests are in applied and computational mathematics with a focus on numerical analysis and mathematical modeling of multiphysics phenomena. I am confident that the experience and skills I gain from being involved in this project will significantly enhance my ability to make meaningful contributions to both my current research and future professional pursuits. My ongoing PhD research, “Modeling and Numerical Analysis in Cryosphere” focuses on modeling processes in cold regions and in the Arctic, which takes advantage of a lot of experimentally collected data. This research continues from work that began as my Master's capstone project. I am particularly interested in applications in climate science related to the cryosphere, such as thermal conduction and fluid flow in cold regions. I mainly work with finite volumes and use Matlab at an advanced level for coding purposes. Additionally, I also worked and had experience with R, Maple, SPSS, Python, and C. I would also like to work with computational methods and implement them in scientific computing environments. Additionally, I am interested in high performance computing and the simulation of large-scale, data-driven models that support the understanding of climate related processes. In July 2023, I attended the Applied Mathematics Skills Improvement for Graduate Studies Advancement (AMIGAs) program at IPAM, UCLA. During this program, I gained experience in computational skills such as statistics, optimization, and machine learning. I participated in professional development activities and research talks focused on the mathematics of data science and its applications. The tutorials covered skills in computer programming, mathematical modeling, and data management. In particular, I completed several courses from DataCamp, including Machine Learning with scikit-learn, as well as courses in Python and R. In October 2024, I had the privilege of attending the SIAM MDS 2024 conference, where I participated in the ''Hands on HPC for MDS'' workshop and had the opportunity to get hands-on experience using ORNL’s exascale supercomputer, Frontier. This workshop taught me how to run large-scale simulations on a supercomputer. This experience has greatly improved my understanding of the strengths and challenges of working with advanced HPC systems. In June 2025, I participated in the Structure-Preserving Scientific Computing and Machine Learning: Summer School and Hackathon at University of Washington, Seattle. The program focused on the structure-preserving numerical methods and machine learning, featuring lectures and hands on tutorials led by experts in computational mathematics. As part of the hackathon, I collaborated with fellow students on the project ''Developing Physics-Informed Preconditioners for a Thermal Radiative Transfer Model'' led by Dr. Terry Haut from Lawrence Livermore National Laboratory (LLNL). This experience deepened my understanding of advanced numerical methods and further strengthened my skills in teamwork, scientific computing, and problem solving in a challenging research environment. As a researcher in applied and computational mathematics modeling of multiphysics phenomena, my future plans involve developing and simulating complex, efficient, large-scale computational models, particularly in thermal conduction and fluid interactions, which handle vast datasets and require high performance computing resources to solve effectively. I believe that being involved in a NAIRR or HPSF project will help to improve my skills and provide the knowledge I need to achieve my goals. Being involved in a NAIRR or HPSF project would be a great opportunity for me in many ways. This project experience would be heavily supported to enhance my ongoing PhD research and also to improve me as an independent advanced researcher. Apart from contributing to the project, I am looking forward to networking with other scientists and students. I am happy to learn important people’s skills so I can later volunteer and help others. I would regard applying to the NSF National AI Research Resource (NAIRR) pilot and the High Performance Software Foundation (HPSF) projects as a valuable opportunity to learn and further develop my skills. I would like my application to be considered for both NAIRR and HPSF projects, but I prefer HPSF projects more, as they align more closely with my research interests. I believe that being involved in NAIRR or HPSF project would help me with an ideal environment to advance as a researcher in my field. Thank you very much for considering my application.

Lightning Talk Title

Coupled snow-soil model

Keywords (Maximum 20 words)

Surface energy balance; Permafrost; Snow; Radiation; Modeling: Alaskan Arctic; Finite volume methods; Domain Decomposition; ML/NN regression model; Sobol sensitivity analysis.