Dr. Johannes Krotz | Computational Methods | Best Researcher Award

Postdoctoral Fellow at Notre Dame, United States

 Profiles

• Google scholar
• Scopus
• Orcid
• Research Gate

Summary

👨‍🎓 PhD candidate in Mathematics with a minor in Computer Science, specializing in probabilistic and data-driven methods for numerical PDEs and hybrid Monte Carlo methods for complex systems simulations. Experienced in statistical modeling, computational physics, and advanced simulations with a strong background in teaching and academic leadership. Currently working as a Postdoctoral Researcher at the University of Notre Dame.

 Education

🎓 PhD in Mathematics (Minor in CS)
University of Tennessee Knoxville, 2021–2024

• Dissertation on Probabilistic & Data-Driven Methods in Numerical PDEs
• GPA: 4.0

📊 M.Sc. in Statistics
University of Tennessee, 2022–2024

• GPA: 3.9

📚 M.Sc. in Mathematics
Oregon State University, 2019–2021

• GPA: 4.0

⚛️ M.Sc. in Physics
University of Konstanz, 2015–2019

• GPA: 4.0 (Honors)

🔢 B.Sc. in Mathematics & Physics
University of Konstanz, 2012–2018

• GPA: 3.5 (Mathematics), 3.3 (Physics)

 Professional Experience

🔬 Postdoctoral Researcher
University of Notre Dame, 2024–Present

• Research on hybrid Monte Carlo & deterministic kinetic transport algorithms for exascale simulations in neutron transport.

🧑‍💻 Graduate Research Assistant (GRA)
University of Tennessee/ORNL, 2023–2024

• Advancing dynamic likelihood filters for stochastic advection-diffusion equations in collaboration with ORNL and UTK.

💼 Research Intern
Oak Ridge National Lab (ORNL), 2021–2022

• Developed hybrid algorithms for simulating complex particle systems in 2D & 3D.

🌍 Research Intern
Los Alamos National Lab (LANL), 2020

• Focus on high-fidelity discrete fracture networks and Poisson-disk sampling algorithms for triangulations.

 Research Interests

• 🧠 Computational Mathematics: Hybrid Monte Carlo methods, kinetic transport equations, and numerical simulations for complex physical systems.
• 🔍 Stochastic Processes: Advanced data-driven filtering techniques and applications in fluid dynamics, advection-diffusion, and PDEs.
• 💻 Statistical Modeling: Development of methods for high-dimensional data and stochastic modeling.
• 🌐 Interdisciplinary Work: Collaborating across fields of mathematics, physics, and engineering to tackle real-world computational challenges.

🏆 Awards

• 1st & 3rd place at the UTK SIAM Research Showcase (2023, 2024)
• Randall E. Cline Award (2022) for research excellence

🖥 Technical Skills

• Python, C++, R, Matlab, LATEX, and more
• Basic Fortran, AWK

🔗 Professional Memberships

• SIAM, AWM, AAAS, UCW

 Publications

A Hybrid Monte Carlo, Discontinuous Galerkin Method for Linear Kinetic Transport Equations

• Authors: Johannes Krotz, Cory D. Hauck, Ryan G. McClarren
• Journal: Journal of Computational Physics, Vol. 514
• Year: 2024

Variable Resolution Poisson-Disk Sampling for Meshing Discrete Fracture Networks

• Authors: Johannes Krotz, Matthew R. Sweeney, Jeffrey D. Hyman, Juan M. Restrepo, Carl W. Gable
• Journal: Journal of Computational and Applied Mathematics, Vol. 407
• Year: 2022

Dynamic Likelihood Filters for Advection Diffusion Equations

• Authors: Johannes Krotz, Jorge M. Ramires, Juan M. Restrepo
• Journal: The Monthly Weather Review
• Year: Under review

Minimizing Effects of the Kalman Gain on Posterior Covariance Eigenvalues, the Characteristic Polynomial and Symmetric Polynomials of Eigenvalues

• Authors: Johannes Krotz
• Journal: Arxiv (preprint)
• Year: 2024