I am Jorge (George) Chumbipuma, a Ph.D. student in Computational & Applied Mathematics at Rice University, advised by Dr. Beatrice Riviere. I work on numerical methods for time-dependent partial differential equations, with an emphasis on numerics-informed neural solvers.

I extend Numerics-Informed Neural Networks (NINNs) for parabolic PDEs, a method introduced by Celaya, Kirk, Fuentes, and Riviere (2024). The network is trained on a discrete residual with fixed finite-difference operators, and Dirichlet conditions are enforced exactly by boundary lifting. Details and publications are on the Research page.

Current support is the NDSEG Fellowship (Department of Defense, September 2025 – August 2028) and the Ken Kennedy Institute 2025/26 ExxonMobil Graduate Fellowship. I was an HSF Scholar (Hispanic Scholarship Fund, 2025) and previously held the GEM Employer Sponsored Fellowship (National GEM Consortium, sponsored by MIT Lincoln Laboratory, 2024).

Education · Experience · Leadership · Talks · Workshops

Education

Rice University

Houston, TX

Ph.D., Computational and Applied Mathematics

August 2023 – expected May 2028

• Advisor: Dr. Beatrice Riviere
• Courses: Applied Functional Analysis; Advanced Numerical Analysis; Numerical Methods for PDEs; Numerical Linear Algebra; Systems of Equations & Unconstrained Optimization; Modeling Mathematical Physics; High-Performance Computing; Scientific Machine Learning

M.A., Computational and Applied Mathematics (thesis)

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

San José State University

San Jose, CA

M.S., Mathematics

• Advisor: Dr. Slobodan Simić
• Honors: Phi Kappa Phi
• Courses: Numerical PDEs; Numerical Linear Algebra; Advanced Dynamical Systems; Stochastic Processes

University of California, Irvine

Irvine, CA

B.S., Electrical Engineering and Physics (double major)

• Minor: Information and Computer Science
• Honors: Tau Beta Pi
• Courses: Numerical Analysis; Data Structures; Digital Signal Processing; Engineering Probability; Computer Organization; Embedded Computing Systems; Statistical Physics; Mathematical Physics

Experience

• R&D Graduate Summer Intern — Computer Science Research Institute (CSRI), Sandia National Laboratories

  Summer 2026

  I built overlapping-Schwarz software for two-dimensional advection–diffusion: finite-difference or NINN solvers on each subdomain, coupled through interface data, including time-window marching. Mentored by Dr. Irina Tezaur. This coupling is arXiv:2609.17841. See Research.

• Scientific Computing Intern — Lawrence Livermore National Laboratory

  Summer 2025

  I implemented a RAJA dense-constraint driver with MPI in HiOp, added MAGMA GPU linear-algebra paths alongside LAPACK, and configured GPU tests on Lassen (IBM Power9 + NVIDIA V100) with ctest, jsrun, and TotalView. See Research.

• Owl Edge Externship — Computational Science, Oak Ridge National Laboratory

  March 2025

  I shadowed computational scientists, including a Frontier supercomputer tour, with host Dr. Shuo Qian.

• Summer Research Intern — MIT Lincoln Laboratory

  Summer 2024

  I built MATLAB models of Intelligence, Surveillance, and Reconnaissance (ISR) and tactical system performance and ran scenario sweeps over mission parameters.

Leadership, mentoring, and teaching

Leadership

• Vice President, Rice University SIAM Student Chapter

  2026–2027

  I serve as Vice President and maintain the chapter website (events, SIAM meetings, internships and fellowships, and newsletter materials).

Mentoring

• Peer Mentor, Ph.D. Peer Mentoring Program

  Rice University Center for Engineering Excellence Through Equity · October 2025 – present

  I mentor a Ph.D. student in the George R. Brown School of Engineering and Computing.

• Invited panelist, Fellowship Guidance

  Gulf Coast Undergraduate Research Symposium (GCURS), Rice University · October 2025

  I represented NDSEG on a fellowship panel with NSF GRFP, Fulbright, Hertz, and Goldwater.

• Peer Mentor, SACRED Mentoring Program / MAS Circle

  SACNAS · March 2025 – September 2025

  I mentored a student transitioning to graduate-level mathematics through SACNAS’s Mentorship Activated by SACNISTAs (MAS) Circle.

Teaching

• Founder & Lead Educator, Pumatics

  January 2022 – present

  Math, science, computer science, and test-prep tutoring; see Tutoring.

Selected presentations

• Numerics-Informed Neural Networks for PDE Solvers: Error Bounds and Pretrained Models for Schwarz Domain Decomposition

  Oral presentation · Technical Presentation Competition, 50th Annual GEM Conference, Dallas, TX · September 2026

• Numerics-Informed Neural Networks for Parabolic Partial Differential Equations

  Poster · International Congress of Mathematicians (ICM 2026), Philadelphia, PA · July 2026

• Numerics-Informed Neural Networks for Parabolic Partial Differential Equations

  Contributed presentation · 2026 SIAM Annual Meeting (AN26), Cleveland, OH · 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. One of seven lightning speakers.

• 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

Conferences and workshops

• SIAM Texas–Louisiana Sectional Meeting — Participant, Austin, TX, September 2025
• Scientific Machine Learning for Differential Equations Workshop — Participant, 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