About Me

Hi! I am Juan Felipe Osorio Ramirez, a third-year PhD student in Applied Mathematics at the University of Washington, where I study the mathematics of data science and its role in solving and learning PDEs, particularly in physics-informed modeling and the emerging field of scientific machine learning using kernel methods. I am fortunate to work under the supervision of Prof. Bamdad Hosseini.

My current research includes:

• Learning/discovery of PDEs using GP/kernel methods with applications in planetary sciences and sismic data.

• Solving Keller-Segle type equations using kernel methods.

During 2024-25 academic year, I will be the co-Lead Teaching Assistant for the Deparment of Mathematics at the University of Washington.

Education

• Ph.D. in Applied Mathematics, 2022-2026 (expected) @ Department of Applied Mathematics, University of Washington.

• M.Sc. in Applied and Computational Mathematics, 2021-2022 @ Department of Applied Mathematics, University of Washington.

• B.Sc. in Statistics, 2017-2021 @ Department of Statistics, Universidad Nacional de Colombia.

• B.Sc. in Mathematics, 2013-2017 @ Department of Mathematics, Escuela Colombiana de Ingeniería Julio Garavito.

Publications

• Jalalian, Y., Osorio, J. F., Hsu, A., Hosseini, B., & Owhadi, H. (2025). Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis. arXiv preprint arXiv:2503.01036. see here and code here.

• Gallego, J.A., Osorio, J. F., & González, F.A. (2022). Fast Kernel Density Estimation with Density Matrices and Random Fourier Features. see here

• Agredo, Julián & Leon, Y. & Osorio, J. F. & Peña, A.. (2019). Buzano’s inequality in algebraic probability spaces. Journal of Mathematical Inequalities. 585-599. 10.7153/jmi-2019-13-38. see here

Teaching assistant

• 24-SP: AMATH563-Inferring Structure of Complex Systems

• 24-WI: AMATH582-Computational Methods for Data Analysis

• 23-AU: AMATH501-Vector Calculus and Complex Variables

• 23-SP: AMATH583-High-Performance Scientific Computing

• 23-WI: MSC Tutor in calculus, linear algebra and differential equations.

• 22-AU: MATH124-Calculus with Analytic Geometry I

Conferences/Posters/Workshops

• 25-WI-(C

  P): Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis. LatMath 2025. IPAM/UCLA.

• 24-SU-(P): Data-Efficient RKHS Methods for Learning Differential Equations: Algorithms and Error Analysis. University of Bath, UK.

• 24-WI-(C): Kernel methods for learning PDEs. SIAM UQ 24. Italy.

• 23-SU-(W): Introduction to Scientific Machine Learning (3 days) at MindLab Bogotá, Colombia. See more here.

Conferences/Workshops attended

• LatMath 2015. University of California in Los Angeles. Los Angeles, US.

• Machine Learning in Infinite Dimensions. University of Bath. Bath, UK.

• 2024 SIAM Conference on Uncertainty Quantification. Trieste, Italy.

• 2023 SIAM Conference on Optimization. Seattle, USA.

Awards

• LatMath Graduate Student Poster Session Winner: Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis. LatMath 2025. IPAM/UCLA.

Events organized

• Minisymposium on GPs and Kernel Methods for Scientific Machine Learning at SIAM UQ 2024 in Trieste, Italy.