About Me

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Hi, thanks for stopping by! I am Juan Felipe Osorio Ramirez, a fourth-year PhD candidate 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.

News

  • Open to Summer 2026 Internship Opportunities in ML/AI, Data Science, or Quantitative research.

  • I will be giving a talk at SIAM-PNW 2025 (Seattle,US) on using kernel methods for learning and emulating PDEs.

  • I will be giving a talk at SIAM-PDE 2025 (Pittsburgh,US) on characterizing Jupiter’s radiation belt through PDEs using SciML kernel methods.

Current research projects

  • Learning stochastic PDEs in finance using kernel methods.

  • Learning/discovery of PDEs using GP/kernel methods with applications in planetary sciences (Jupiter’s radiation belt) and sismic data.

  • Scalability of kernel methods for learning systems of PDEs using distributed methods in optimization.

  • Solving time-dependent PDEs using kernel methods including Fokker-Planck and Keller-Segle models.

Education

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

  • 25-AU: AMATH581-Intro to Scientific Computing

  • 24-25: Co-Lead Teaching Assistant for the Deparment of Mathematics at the University of Washington.

  • 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-AU-(C): Uncovering Jupiter’s Radiation Belt Through PDE Learning. SIAM-PDE 2025. Pittsburgh, United States.

  • 25-AU-(C): Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators. SIAM-PNW 2025. University of Washington.

  • 25-WI-(C P): Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis. LatMath 2025. IPAM at University of California, LA.

  • 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 Scientific Machine Learning at SIAM PNW 2025 in Seattle, United States.

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