About

About

I am Jorge (George) Chumbipuma, a Ph.D. student in Computational & Applied Mathematics at Rice University, working on numerical methods for PDEs with applications in scientific machine learning. My advisor is Dr. Beatrice Riviere.

Research Interests

My research lies at the intersection of scientific machine learning (SciML) and numerical methods.

I study and extend Numerics-Informed Neural Networks (NINNs) — time-marching neural solvers for parabolic PDEs introduced by Celaya, Kirk, Fuentes, and Riviere (2024) — focusing on boundary lifting, training schedules, stability, error propagation, and convergence relative to classical schemes such as Backward Euler and Crank–Nicolson. More recently, at Sandia National Laboratories, I have built research software to evaluate hybrid neural / full-order couplings that build on prior Schwarz–PINN ideas.

I implement and run computations on HPC clusters (Rice NOTs) and have experience with GPU computing and distributed algorithms from internships at Sandia National Laboratories and Lawrence Livermore National Laboratory.

Earlier interests in porous media and fracture modeling continue to influence my perspective on multiscale, multiphysics problems.

My research is supported by the NDSEG Fellowship (Department of Defense), GEM Fellowship (sponsored by MIT Lincoln Laboratory), and the Ken Kennedy Institute ExxonMobil Graduate Fellowship. You can explore my ongoing projects, thesis, and related publications on the Research page.

Experience

  • Computational Science Intern – Sandia National Laboratories (Summer 2026)
    Studied hybrid neural / full-order PDE coupling with overlapping Schwarz methods. Built a research code lab for finite-difference, NINN, and PINN baselines and ran experiment campaigns under the mentorship of Irina Tezaur and collaborators, adapting methods introduced in prior Sandia and Rice work rather than inventing those frameworks.

  • Scientific Computing Intern – Lawrence Livermore National Laboratory (Summer 2025)
    Worked on GPU-enabled optimization in the HiOp framework: implemented RAJA-based solvers with MPI support and ported quasi-Newton methods to CUDA.

  • Summer Research Intern – MIT Lincoln Laboratory (Summer 2024)
    Conducted research on modeling and analysis of Intelligence, Surveillance, and Reconnaissance (ISR) systems. Developed mathematical models and implemented simulations in MATLAB to analyze system behavior under varied mission parameters.

Presentations

  • Numerics-Informed Neural Networks for Parabolic PDEs (Talk), 2026 SIAM Annual Meeting (AN26), July 2026
  • Numerics-Informed Neural Networks for Parabolic PDEs (Lightning talk and poster), Energy HPC & AI Conference, Ken Kennedy Institute, Rice University, Houston, TX, February 2026
  • Scientific Machine Learning for Geophysical PDEs (Poster), SIAM Conference on Mathematical & Computational Issues in the Geosciences (GS25), Louisiana State University, Baton Rouge, LA, October 2025
  • Numerics-Informed Neural Networks for Parabolic PDEs (Poster), RTG NASC Annual Workshop, Rice University, Houston, TX, October 2025
  • Numerical Solutions to the Nonlinear Vlasov Equations, Rice University, Houston, TX, May 2024

Teaching, Mentoring, and Outreach

I am committed to education and mentorship, especially for underrepresented groups in STEM.

Mentoring

  • Peer Mentor — PhD Peer Mentoring Program, Rice University Center for Engineering Excellence Through Equity (October 2025 — Present)
    Mentoring a PhD student in the George R. Brown School of Engineering and Computing through a formal university-sponsored peer mentoring program.

  • Peer Mentor — SACRED Mentoring Program, Society for Advancement of Chicanos/Hispanics & Native Americans in Science (SACNAS) (March 2025 — September 2025)
    Mentored a Latina student transitioning to graduate-level mathematics through SACNAS’s Mentorship Activated by SACNISTAs (MAS) Circle, providing biweekly check-ins, academic guidance, and resources toward her PhD goal.

  • Fellowship Panel Discussion, Gulf Coast Undergraduate Research Symposium (GCURS), Rice University (October 2025)
    Invited panelist representing NDSEG alongside panelists from NSF GRFP, Fulbright, Hertz, and Goldwater fellowships. Shared insights on fellowship application processes and opportunities.

Teaching

  • Founder & Lead Educator — Pumatics (January 2022 — Present)
    Operate a tutoring service offering instruction in math, science, computer science, and test preparation. Learn more on the Tutoring page.

Conferences and Workshops

  • 2026 SIAM Annual Meeting (AN26) — Presenter, July 2026
  • Energy HPC & AI Conference — Presenter (lightning talk and poster), Rice University, Houston, TX (February 2026)
  • SIAM Conference on Mathematical & Computational Issues in the Geosciences (GS25) — Presenter, Baton Rouge, LA (October 2025)
  • SIAM Texas-Louisiana Sectional Meeting — Participant, Austin, TX (September 2025)
  • Scientific Machine Learning for Differential Equations Workshop — Participant, The Oden Institute, Austin, TX (September 2025)
  • Firedrake USA 2025 Workshop — Participant, Waco, TX (February–March 2025)
  • Blackwell–Tapia Conference — Participant, ICERM @ Brown University, Providence, RI (November 2024)
  • GEM 2024 Annual Conference — Participant, San Antonio, TX (September 2024)
  • SACNAS CareerCon 2024 — Participant, Remote (March 2024)

Education

Rice University, Houston, TX

Doctor of Philosophy – Computational and Applied Mathematics
August 2023 – May 2028 (Expected)

  • Fellowships: NDSEG, GEM, Ken Kennedy Institute ExxonMobil Graduate Fellowship
  • Advisor: Dr. Beatrice Riviere
  • Key Courses: Functional Analysis, Advanced Numerical Analysis, Modeling Mathematical Physics, High-Performance Computing, Scientific Machine Learning

Master of Arts – Computational and Applied Mathematics
December 2025

  • Thesis: Numerics-Informed Neural Networks for Parabolic Partial Differential Equations
  • Advisor: Dr. Beatrice Riviere
  • Committee: Dr. Lu Zhang, Dr. Thomas Anderson

San José State University, San Jose, CA

Master of Science – Mathematics
August 2020 – August 2022

  • Honors: Phi Kappa Phi
  • Advisor: Dr. Slobodan Simić
  • Key Courses: Advanced Matrix Theory, Numerical Partial Differential Equations, Stochastic Processes, Numerical Linear Algebra
  • Research: Applied dynamical systems techniques to analyze stability in cosmological models within the Lambda Cold Dark Matter (ΛCDM) framework.

University of California, Irvine, Irvine, CA

Bachelor of Science – Double Major in Electrical Engineering and Physics
Minor: Information and Computer Science

  • Honors: Tau Beta Pi
  • Key Courses: Data Structures, Numerical Analysis, Statistical Physics, Engineering Probability, Machine Vision, Computer Organization

Future Goals

I aim to become a Research Computational Scientist at a national laboratory, working on scientific computing and numerical methods. I am interested in developing computational methods for complex physical systems and contributing to large-scale scientific simulations.