Mohammad, Rhudaina

Associate Professor

rmohammad@math.upd.edu.ph

Math Building 215

Research Interests
numerical analysis・calculus of variations・partial differential equations・neural network theory and applications・mathematical cell biology・interface evolution (multiphase) problems

Academic Groups

Numerical Analysis and Scientific Computing (head)
Optimization and Approximation (affiliate)

Education
- PhD Mathematics 博士(理学)
  Kanazawa University (金沢大学), Japan
  Dissertation: Numerical Analysis of Multiphase Curvature-driven Interface Evolution with Volume Constraint (体積保存条件を満たす複数の界面の曲率による運動の数理解析)
  Adviser: Dr. Karel Švadlenka
- MS Mathematics
  University of the Philippines Diliman
  Thesis: Amrein-Berthier’s Uncertainty Principle
  Adviser: Dr. Noli N. Reyes
- BS Mathematics, Cum Laude
  Western Mindanao State University
- Professional Education Certificate Program, LPT (Licensed Professional Teacher)
  Western Mindanao State University
Postdoctoral Fellowships
- Department of Mathematics, Kyoto University (京都大学), Japan (JSPS Postdoctoral Fellowship for Research)
  Supervisor: Dr. Karel Švadlenka (April 2018 - July 2020)
  Project: Theory and Applications of Anisotropic Interfacial Network Evolution (https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18F18016)
Research
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 Students
1. Margaret Esther C. Cruz, PhD Data Science
  Dissertation Proposal: “Image Reconstruction in Electrical Impedance Tomography using Physics-Informed Neural Networks with Differential Evolution”
  co-adviser: Dr. Renier G. Mendoza
2. Jeffer Dave Cagubcob, PhD Mathematics, on hold for qualifying exam
  co-adviser: Dr. Julius Fergy Rabago (Kanazawa University, Japan)
3. Christian Matthew Tandingan, PhD Mathematics, on hold for qualifying exam
  co-advisers: Dr. Gervy Marie Angeles, Dr. John Sebastian Simon (Universität Koblenz, Germany)
4. Ken Matthew C. Oliva, PhD Mathematics, D2 coursework in progress
  co-advisers: Dr. Bituin Cabarrubias, Dr. Aurelio de los Reyes V
5. Jose Aries B. De Los Santos, PhD Data Science, D1 coursework in progress
Current MS Students
1. Gwhyneth De Guzman, MS Applied Mathematics (OA Track)
  Thesis Proposal: “Optimal Placement of Low Impact Development Controls in Urban Storm Water Drainage System”
  co-adviser: Dr. Arrianne Crystal Velasco
2. Rito Joseph F. Dominado, MS Applied Mathematics (MLPS Track)
  Thesis Proposal: “Reaction Network Analysis of Apoptosis Models”
  co-adviser: Dr. Bryan S. Hernandez
3. Conie Q. Janul, MS Applied Mathematics (OA Track), on maternity leave
  Thesis Proposal: “Modeling and Optimal Control of Pestalotiopsis Leaf Fall Disease in Basilan Rubber Plantation”
  co-adviser: Dr. Aurelio de los Reyes V
4. A C Bernadette M. Ducusin, MS Applied Mathematics (MF Track)
  co-adviser: Dr. Rachelle R. Sambayan
5. Russell Fitzgerald L. Santos, MS Applied Mathematics (NADE Track), M2 coursework in progress
  co-adviser: Dr. Rachelle R. Sambayan
6. Aarhus M. Dela Cruz, MS Applied Mathematics (OA Track), M2 coursework in progress
  co-adviser: Dr. Jose Ernie C. Lope
7. Lem Nathan C. Ereña, MS Applied Mathematics (NADE Track), M2 coursework in progress
  co-adviser: Dr. Hirofumi Notsu (Kanazawa University, Japan)
Current Undergraduate Students
1. Jeremiah Daniel A. Regalario, BS Mathematics
2. Patrick D. Zuñiga, BS Mathematics
3. Aliza Marie M. Casimsiman, BS Mathematics
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Former DOST-CIP Fellow
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
1. Jose Aries B. De Los Santos, MS Applied Mathematics (OA Track), S1 2024-25
  Thesis: “Perturbed Accelerated Gradient Method with Adaptive Learning Rate”
  co-adviser: Dr. Renier Mendoza
2. 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“
3. Ken Matthew C. Oliva, MS Applied Mathematics (OA Track), S2 2022-23
  Thesis: “Numerical simulation of the 2020 Taal volcanic ash dispersion”
  co-advisers: Dr. Arrianne Crystal Velasco, Dr. Renier G. Mendoza
4. 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-adviser: Dr. Jose Ernie C. Lope
5. Paul Gabriel E. Lerona, MS Chemical Engineering, S1 2022-23
  Thesis: “Simulation of solidification of titanium-base binary alloy using phase-field modeling”
  co-adviser: Dr. Bryan G. Alamani (UP Department of Chemical Engineering)
Former Undergraduate Students
1. Ronmykel Angelo M. Paglinawan, BS Mathematics, Midyear 2025
  Thesis: “A Mathematical Model for Inflammation Propagation based on a Reaction-Diffusion System”
  co-adviser: Dr. Gervy Marie Angeles
2. Maxine T. Darvin, BS Mathematics, S2 2024-25
  Thesis: “Spatiotemporal Analysis of Pestalotiopsis Infection in Basilan Rubber Plantations using Remote Sensing and Random Forest“
3. Lem Nathan C. Ereña, BS Mathematics, S2 2023-24
  Thesis: “Markov Chain Monte Carlo Approximation of Volume-preserving Mean Curvature Flow and Its Application to Cell Sorting“
4. Vince Patrick L. Roque, BS Mathematics, S2 2022-23
  Thesis: “Solving Ordinary Differential Equations: An Artificial Neural Network Approach“
5. Rachel Noelle D. Carrido, BS Mathematics, Midyear 2022
  Magna Cum Laude
  Thesis: “A Total Variation Approach to Image Inpainting“
Teaching
Current Courses:
- Math 171 : Introduction to Numerical Analysis
- Math 209.1 : Selected Topics in Applied Mathematics
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Previous Courses Taught (UP Diliman):

As Faculty Member of the Institute of Mathematics
1. Math 296 : Graduate Seminar
2. Math 271.1 : Numerical Analysis I
3. Math 227 : Calculus of Variations
4. Math 209.1 : Selected Topics in Applied Mathematics
5. Math 171 : Introduction to Numerical Analysis
6. Math 122 : Differential Equations and Applications
7. Math 21 : Elementary Analysis I
As Affiliate Faculty Member of the CS Data Science Program
1. DS 397 : Advanced Mathematical Methods in Data Science
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EXTENSION ACTIVITIES
- Resource Person on 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., April 14-15, 2025, Institute of Mathematics, UP Diliman
- 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
- Member, Scientific Committee, CoMaDS 2025: International Workshop on Computational and Mathematical Methods in Data Science, 3-5 April 2025, Boracay, Philippines
- 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
Publications
1. 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
2. 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
3. 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
4. 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
5. 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.
6. 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
7. 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.
8. 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

Mohammad, Rhudaina

Maryam Mirzakhani, first female Fields Medalist

MENTORING ACTIVITIES

Current PhD Students

Current MS Students

Current Undergraduate Students

Former DOST-CIP Fellow

Former Graduate Students

Former Undergraduate Students

Current Courses:

Previous Courses Taught (UP Diliman):

As Faculty Member of the Institute of Mathematics

As Affiliate Faculty Member of the CS Data Science Program

EXTENSION ACTIVITIES

University

Affiliations