About Me
News
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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.
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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.
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I will be giving a talk at SIAM Mathematics of Data Science 2026. Salt Lake City, United States.
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I will be giving a talk at AGU Annual Meeting 2026. San Francisco, United States.
Current research projects
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Learning/discovery of PDEs using GP/kernel methods with applications in planetary sciences and sismic data.
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Scalability of kernel methods for learning systems of PDEs, and general computational DAGs.
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Solving time-dependent problems using kernel methods including Fokker-Planck and Keller-Segle models in 2D and 3D.
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Uncertainty quantification for Computational Graph Completion, including PDE constrained estimators.
Education
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Ph.D. in Applied Mathematics, 2022-2027 (expected) @ Department of Applied Mathematics, University of Washington.
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M.Sc. in Applied and Computational Mathematics, 2021-2022 @ Department of Applied Mathematics, University of Washington.
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B.Sc. in Statistics, 2017-2021 @ Department of Statistics, Universidad Nacional de Colombia.
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B.Sc. in Mathematics, 2013-2017 @ Department of Mathematics, Escuela Colombiana de Ingeniería Julio Garavito.
Publications
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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.
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Gallego, J.A., Osorio, J. F., & González, F.A. (2022). Fast Kernel Density Estimation with Density Matrices and Random Fourier Features. Springer chapter
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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
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(Talk): Scalable Kernel Methods for Scientific Computing, with Guarantees. NASA Jet Propulsion Laboratory 2026. Pasadena, United States.
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(Talk): Métodos kernel para la solución, aprendizaje y emulación de EDPs. Universidad Escuela Colombiana de Ingeniería Julio Garavito. Bogotá, Colombia.
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(Talk): Operator Learning via Equation Learning. ILAS 2026. Virginia Tech. Blacksburg, United States.
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(Talk): Uncovering Jupiter’s Radiation Belt Through PDE Learning. SIAM-PDE 2025. Pittsburgh, United States.
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(Poster): Kernel methods for Learning Differential Equations and Operator Learning. IMSI 2025. Chicago, United States.
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(Talk): Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators. SIAM-PNW 2025. University of Washington. Seattle, United States.
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(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.
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(Poster): Data-Efficient RKHS Methods for Learning Differential Equations: Algorithms and Error Analysis. University of Bath. Bath, United Kingdom.
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(Poster): Kernel methods for learning PDEs. SIAM Uncertainty Quantification 2024. Trieste, Italy.
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(Workshop organizer): Introduction to Scientific Machine Learning (3 days) at MindLab Bogotá, Colombia. See more on GitHub.
Conferences/Workshops attended
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International Linear Algebra Society. Virginia Tech. 2026. Blacksburg, United States.
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Kernel Methods in Uncertainty Quantification and Experimental Design conference. IMSI 2025. Chicago, United States.
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Scientific Machine Learning. IPAM 2025. UCLA. Los Angeles, United States.
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LatMath 2025. UCLA. Los Angeles, United States.
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Machine Learning in Infinite Dimensions. University of Bath. Bath, United Kingdom.
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2024 SIAM Conference on Uncertainty Quantification. Trieste, Italy.
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2023 SIAM Conference on Optimization. Seattle, United States.
Awards
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Boeing Excellence Award for Research in Applied Mathematics 2026. University of Washington.
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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
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Minisymposium on Scientific Machine Learning at SIAM PNW 2025 in Seattle, United States.
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Minisymposium on GPs and Kernel Methods for Scientific Machine Learning at SIAM UQ 2024 in Trieste, Italy.
Teaching assistant appointments
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26-AU: AMATH581-Introduction to Scientific Computing
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26-SP: AMATH563-Inferring Structure of Complex Systems
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26-WI: AMATH482-Computational Methods for Data Analysis
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25-AU: AMATH581-Introduction to Scientific Computing
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24-25: Co-Lead Teaching Assistant for the Deparment of Mathematics at the University of Washington.
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24-SP: AMATH563-Inferring Structure of Complex Systems
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24-WI: AMATH582-Computational Methods for Data Analysis
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23-AU: AMATH501-Vector Calculus and Complex Variables
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23-SP: AMATH583-High Performance Scientific Computing
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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.
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22-AU: MATH124-Calculus with Analytic Geometry I
Sports
- Weighlifting.