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.

Research Interests

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

I develop and analyze Neural-Informed Neural Networks (NINNs) — time-marching neural solvers for parabolic PDEs — and compare them against traditional methods such as Backward Euler and Crank–Nicolson. My work focuses on stability, error propagation, and convergence in neural PDE frameworks.

I implement and run computations on HPC clusters (Rice NOTs) and have experience with GPU computing and distributed algorithms from my internship at 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) and GEM Fellowship (sponsored by MIT Lincoln Laboratory). You can explore my ongoing projects and research on the Research page.

Experience

  • 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

  • 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

  • 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)

  • GPA: 3.96/4.0
  • Fellowships: NDSEG, GEM
  • Advisor: Dr. Beatrice Riviere
  • Key Courses: Functional Analysis, Advanced Numerical Analysis, Modeling Mathematical Physics, High-Performance Computing, Scientific Machine Learning

San José State University, San Jose, CA

Master of Science – Mathematics
August 2020 – August 2022

  • GPA: 3.9/4.0
  • 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.