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About Me

Juan Felipe Osorio Ramirez, PhD candidate in Applied Mathematics at the University of Washington
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 and Gaussian Processes. I am fortunate to work under the supervision of Prof. Bamdad Hosseini.

News

  • I will be giving a talk “Towards Scalable Kernel Methods for Learning and Solving Systems of Differential Equations” at the Kernel Approximation and Gaussian Processes: Integrating and Expanding Perspectives Workshop 2026 on Operator learning via Equation Learning. BIRS. Banff, Canada.

  • I will be giving a talk at the Mathematical and Computational Foundations of Digital Twins Workshop 2026. Institut d’Études Scientifiques de Cargèse. Corsica, France.

  • I will be giving a talk at SIAM Mathematics of Data Science 2026. Salt Lake City, United States.

  • I will be giving a talk at AGU Annual Meeting 2026. San Francisco, United States.

Current research projects

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

  • Scalability of kernel methods for learning systems of PDEs, and general computational DAGs.

  • Solving time-dependent problems using kernel methods including Fokker-Planck and Keller-Segle models in 2D and 3D.

  • Uncertainty quantification for Computational Graph Completion, including PDE constrained estimators.

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. arXiv preprint and GitHub repository.

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

  • 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. Journal of Mathematical Inequalities

Other projects

  • Pricing an Asian Call Option: Monte Carlo vs. PDE Approach. Quantitative Finance Bootcamp. The Erdös Institute.

Internships

  • NASA Jet Propulsion Laboratory. JVSRP. Summer 2026. Supervised by Brian Zhu and Jouni Jouni Susiluoto. Studying radiation around Jupiter using Machine Learning based models.

Talks and posters

  • (Talk): Scalable Kernel Methods for Scientific Computing, with Guarantees. NASA Jet Propulsion Laboratory 2026. Pasadena, United States.

  • (Talk): Métodos kernel para la solución, aprendizaje y emulación de EDPs. Universidad Escuela Colombiana de Ingeniería Julio Garavito. Bogotá, Colombia.

  • (Talk): Operator Learning via Equation Learning. ILAS 2026. Virginia Tech. Blacksburg, United States.

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

  • (Poster): Kernel methods for Learning Differential Equations and Operator Learning. IMSI 2025. Chicago, United States.

  • (Talk): Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators. SIAM-PNW 2025. University of Washington. Seattle, United States.

  • (Poster): Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis. LatMath 2025. IPAM at UCLA. Los Angeles, United States.

  • (Poster): Data-Efficient RKHS Methods for Learning Differential Equations: Algorithms and Error Analysis. University of Bath. Bath, United Kingdom.

  • (Poster): Kernel methods for learning PDEs. SIAM Uncertainty Quantification 2024. Trieste, Italy.

  • (Workshop organizer): Introduction to Scientific Machine Learning (3 days) at MindLab Bogotá, Colombia. See more on GitHub.

Conferences/Workshops attended

  • International Linear Algebra Society. Virginia Tech. 2026. Blacksburg, United States.

  • Kernel Methods in Uncertainty Quantification and Experimental Design conference. IMSI 2025. Chicago, United States.

  • Scientific Machine Learning. IPAM 2025. UCLA. Los Angeles, United States.

  • LatMath 2025. UCLA. Los Angeles, United States.

  • Machine Learning in Infinite Dimensions. University of Bath. Bath, United Kingdom.

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

  • 2023 SIAM Conference on Optimization. Seattle, United States.

Awards

  • Boeing Excellence Award for Research in Applied Mathematics 2026. University of Washington.

  • 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.

Teaching assistant appointments

  • 26-AU: AMATH581-Introduction to Scientific Computing

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

  • 26-WI: AMATH482-Computational Methods for Data Analysis

  • 25-AU: AMATH581-Introduction 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 at the Math Study Center for general tutoring offered widely to the University of Washington.

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

Sports

  • Weighlifting.