As a member of the Numerical Analysis and Scientific Computing (NASC) Group, my research focuses on three interconnected pillars:

• Mathematical Modeling : development and analysis — including existence, uniqueness, well-posedness, regularity, solution properties — of a mathematical abstraction of a problem or a class of problems, e.g. PDEs, optimization models, variational problems
• Numerical Analysis : mathematical foundation for construction and study — including stability, error analysis, convergence, computational complexity — of a numerical approximation or data-driven solution approach to a mathematically posed problem, e.g., finite element method, gradient-based methods, level set-based methods, neural networks
• Scientific Computing : efficient implementation of proposed numerical methods — harnessing available computational resources, e.g., CRL, UP Data Commons, Saliksik HPC, to address complex problems across life and physical sciences, applied sciences, and engineering

I welcome inquires regarding potential thesis supervision or research collaboration opportunities. Please feel free to contact me to discuss further.

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“I like crossing the imaginary boundaries people set up between different fields — it’s very refreshing. There are lots of tools, and you don’t know which one would work. It’s about being optimistic and trying to connect things.”

Maryam Mirzakhani, first female Fields Medalist

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MENTORING ACTIVITIES

Current PhD Mathematics Students

1. 1. Jeffer Dave Cagubcob, on hold for qualifying exam
      co-advising with Dr. Julius Fergy Rabago (Kanazawa University, Japan)
   2. Ken Matthew C. Oliva, on hold for qualifying exam
      co-advising with Dr. Bituin Cabarrubias
   3. Christian Matthew P. Tandingan, on hold for qualifying exam
      co-advising with Dr. Gervy Marie Angeles, Dr. John Sebastian Simon

Current PhD Data Science Students

1. 1. Camilla Johnine D. Cosme, D1 coursework in progress
   2. Jose Aries B. De Los Santos, D1 coursework in progress
      co-advising with Dr. Karel Svadlenka (Tokyo Metropolitan University, Japan)

Current MS Applied Mathematics Students

1. 1. Lem Nathan C. Ereña, NADE Track, M2 coursework in progress
   2. Aarhus M. Dela Cruz, OA Track, M2 coursework in progress
      co-advising with Dr. Jose Ernie C. Lope

Current Undergraduate Students

1. 1. Aliza Marie M. Casimsiman, BS Mathematics, S1 2026-27
   2. Sofia Ysabelle Liboro, BS Mathematics, S2 2026-27

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Former DOST-CIP Fellow

1. 1. Marian T. Cantal, MS Graduate Fellow in Applied Mathematics
      Assigned Project: “Computational Framework based on a Level Set Formulation for Multiphase Systems”, April 2024 – July 2025

Former Graduate Students in Mathematics

1. 1. Russell Fitzgerald L. Santos, MS Applied Mathematics (NADE Track), S2 2025-26
      Thesis: “Numerical analysis of neural networks with hyperbolic tangent linear unit activation and applications to differential equations”
      co-advised with Dr. Rachelle R. Sambayan
   2. A C Bernadette M. Ducusin, MS Applied Mathematics (MF Track), S2 2025-26
      Thesis: “Modeling Stock Price Data using a Quantum Anharmonic Oscillator Approach”
      co-advised with Dr. Rachelle R. Sambayan
   3. Gwhyneth De Guzman, MS Applied Mathematics (OA Track), S1 2025-26
      Thesis: “Optimal Placement of Low Impact Development Controls in Urban Storm Water Drainage System”
      co-advised with Dr. Arrianne Crystal Velasco
   4. Jose Aries B. De Los Santos, MS Applied Mathematics (OA Track), S1 2024-25
      Thesis: “Perturbed Accelerated Gradient Method with Adaptive Learning Rate”
      co-advised with Dr. Renier Mendoza
   5. Marian T. Cantal, MS Applied Mathematics (NADE Track), S2 2022-23
      Excellence in Graduate Studies Award
      Thesis: “Serrin-type overdetermined boundary problem via level set method“
   6. Ken Matthew C. Oliva, MS Applied Mathematics (OA Track), S2 2022-23
      Thesis: “Numerical simulation of the 2020 Taal volcanic ash dispersion”
      co-advised with Dr. Arrianne Crystal Velasco, Dr. Renier G. Mendoza
   7. Kurt Izak M. Cabanilla, MS Applied Mathematics (OA Track), S1 2022-23
      Excellence in Graduate Studies Award
      Thesis: “Approximation spaces of deep neural networks with ReLU powers”
      co-advised with Dr. Jose Ernie C. Lope
   8. Paul Gabriel E. Lerona, MS Chemical Engineering, S1 2022-23
      Thesis: “Simulation of solidification of titanium-base binary alloy using phase-field modeling”
      co-advised with Dr. Bryan G. Alamani (UP Department of Chemical Engineering)

Former Graduate Student in Data Science

1. 1. Margaret Esther C. Cruz, PhD Data Science, S1 2025-26
      Dissertation: “A Deep Learning-Evolutionary Framework for Image Reconstruction in Electrical Impedance Tomography”
      co-advised with Dr. Renier G. Mendoza

Former Undergraduate Students

Current Courses:

• • Math 209.1 : Selected Topics in Applied Mathematics
  • DS 397 : Data-driven Dynamical Systems

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Previous Courses Taught (UP Diliman):

As Faculty Member of the Institute of Mathematics

1. 1. Math 296 : Graduate Seminar
   2. Math 271.2 : Numerical Analysis II
   3. Math 271.1 : Numerical Analysis I
   4. Math 227 : Calculus of Variations
   5. Math 209.1 : Selected Topics in Applied Mathematics
   6. Math 171 : Introduction to Numerical Analysis
   7. Math 122 : Differential Equations and Applications
   8. Math 21 : Elementary Analysis I

As Affiliate Faculty Member of the CS Data Science Program

1. 1. DS 397 : Advanced Mathematical Methods in Data Science

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EXTENSION ACTIVITIES

• Organizer, CoMFoS-NASC2026 (Conference on Continuum Mechanics Focusing on Singularities, Numerical Analysis, and Scientific Computing), 20-23 June 2026, Lapu-Lapu City, Cebu, Philippines
• Resource Person, “Numerical Methods for Infinite-dimensional Optimization Problems”, SEAMS School on Inverse Problem and Optimal Control, 3-11 December 2025, Baguio City, Philippines
• Resource Person, Mathematical Modeling, Summer Upgrading Program for Mathematics Teachers (SUPMaT 2025), 2-4 June 2025, Zamboanga City, Philippines
• Resource Person, Data Science Workshop of the UP Diliman Mathematics Foundation, Inc., 14-15 April 2025, Institute of Mathematics, UP Diliman
• Member, Scientific Committee, CoMaDS 2025: International Workshop on Computational and Mathematical Methods in Data Science, 3-5 April 2025, Boracay, Philippines
• Resource Person, Training and Workshop on Python Programming and Numerical Methods: An Introduction to Numerical Linear Algebra and Differential Equations, 29-31 January 2025, 2F CCE Building, Visayas State University
• Resource Person, Linear Systems and Applications: A Hands-on Python Workshop, 23-25 May 2024, CSRC, UP Diliman
• Organizer, SEAMS School Manila 2023: Scientific Computing for Differential Equations and Applications, 22 November – 01 December 2023, Institute of Mathematics, UP Diliman
• Organizer, UP World Experts Lecture Series 2023: Interface Evolution Problems, 24 November 2023, Institute of Mathematics, UP Diliman
• Organizer, KU-UPD Joint Seminar on Numerical Analysis and Scientific Computing, 16 October 2023, Online via Zoom
• Member, Local Organizing Committee, SEAMS School Manila 2022: Modern Trends in Signal and Data Processing, 5-13 December 2022, Institute of Mathematics, UP Diliman

1. R.G. Mendoza, R. Mohammad, K.M. Oliva, and A.C. Velasco (June 2026). Modeling the Dispersion of Taal Volcanic Ash Using the Advection–Diffusion Equation. Philippine Journal of Science 155:3. https://philjournalsci.dost.gov.ph/modeling-the-dispersion-of-taal-volcanic-ash-using-the-advection-diffusion-equation/
2. M.E.C. Cruz, R.G. Mendoza, and R. Mohammad (2025). Image reconstruction in electrical impedance tomography using deep neural networks with differential evolution. AIMS Electronic Research Archive 33: 12, 7637–7675. https://doi.org/10.3934/era.2025338
3. K.I. Cabanilla, R. Mohammad, and J.E. Lope (2024). Neural Networks with ReLU Powers Need Less Depth. Neural Networks 172, 106073.  doi: 10.1016/j.neunet.2023.12.027
   
4. R.A. Escosio, O. Cawiding, B. Hernandez, R. Mendoza, V.M. Mendoza, R. Mohammad, C. Pilar-Arceo, P.K. Salonga, F.L. Suarez, P. Sy, T.H. Vergara, A. de los Reyes (2023). A model-based strategy for the COVID-19 vaccine roll-out in the Philippines, Journal of Theoretical Biology 573, 111596. https://doi.org/10.1016/j.jtbi.2023.111596
5. R. Mohammad, H. Murakawa, K. Švadlenka, and H. Togashi (2022). A numerical algorithm for modeling cellular rearrangements in tissue morphogenesis. Communications Biology 5 (1), 239. https://www.nature.com/articles/s42003-022-03174-6
6. N. Shofianah, K. Švadlenka, and R. Mohammad (2017). Numerical method for the simulation of contact angle dynamics. AIP Conf. Proc. 1913, 020020. https://doi.org/10.1063/1.5016654
7. R. Mohammad and K. Švadlenka (2015). Multiphase volume-preserving interface motions via localized signed distance vector scheme. Discrete and Continuous Dynamical Systems – S 8 (5), 969–988. doi: 10.3934/dcdss.2015.8.969.
8. N. Shofianah, R. Mohammad, and K. Švadlenka (2015). Simulation of triple junction motion with arbitrary surface tensions. IAENG International Journal of Applied Mathematics 45 (3), 235–244. https://www.iaeng.org/IJAM/issues_v45/issue_3/IJAM_45_3_09.pdf
9. R. Mohammad and K. Švadlenka (2014). On a penalization method for an evolutionary free boundary problem with volume constraint. Advances in Mathematical Sciences and Applications 24 (1), 85–101. https://mcm-www.jwu.ac.jp/~aikit/AMSA/current.html#fh5co-tab-feature-vertical11.
10. R. Mohammad and N. N. Reyes (2010). Strong annihilation of some closed Hilbert subspaces. Mindanawan Journal of Mathematics vol. 1, pp. 85–94.

For a complete list of journal articles and conference proceedings, visit:

• ORCID: https://orcid.org/0000-0002-9803-4350
• Google Scholar: https://scholar.google.com/citations?user=mnlCvv4AAAAJ&hl=en&authuser=1
• MathScinet: https://mathscinet.ams.org/mathscinet/MRAuthorID/1099553
• Web of Science: https://www.webofscience.com/wos/author/record/ABB-7283-2020
• Scopus: https://www.scopus.com/authid/detail.uri?authorId=56715255900