Filip Bělík

Applied mathematics · Scientific computing

Filip Bělík

PhD Candidate in Applied Mathematics at the University of Utah

I develop computational methods for model reduction, scientific computing, and uncertainty quantification, with applications in dynamical systems and mathematical biology. I am coadvised by Akil Narayan and Christel Hohenegger. I plan to graduate in May 2027.

Curriculum vitae Email Google Scholar GitHub ORCID
Portrait of Filip Bělík

Research

Current work

My research centers on efficient computational models for complex parametric systems, sparse measure approximation, and mathematical models of arterial fluid dynamics.

Reduced basis approximation example

Model reduction · Julia

Parametric Model Order Reduction

I develop efficient reduced-order methods for parametric systems, including greedy algorithms, proper orthogonal decomposition, and balanced truncation.

PreprintJulia packageDocumentation

With Akil Narayan and Yanlai Chen.

Visualization of Carathéodory pruning

Scientific computing · Algorithms

Carathéodory Pruning

I design fast, robust QR-type algorithms that replace a positive discrete measure with a sparse representation while preserving target moments.

PreprintJulia packageDocumentation

With Akil Narayan and Jesse Chan.

Animation of modeled arterial blood flow

Arterial blood flow · Uncertainty quantification

Blood Flow, Conductivity, and Uncertainty

I model arterial flow, wall motion, and red blood cell behavior to study how blood pressure influences electrical measurements at the wrist. Sensitivity analysis identifies the parameters that drive model predictions.

PublicationPreprint

With Christel Hohenegger, Henry Crandall, Benjamin Sanchez, Tyler Schuessler, and Braxton Osting.

Earlier work

  • Closed Vortices as Self-Avoiding PolygonsUndergraduate honors project · Markov chain Monte CarloPresentation
  • Carbon Sequestration in Forests2022 MCM/ICM · Age-structured modelingSubmission
  • Port-and-Sweep Solitaire Army ProblemDiscrete mathematics · Linear algebraBackground
  • Health-Related Habits on TwitterMachine learning · Social networks

Scholarship

Selected publications and preprints

  1. Cuffless hemodynamic monitoring with physics-informed machine learning models

    H. Crandall, T. Schuessler, F. Bělík, et al. Nature Communications, 2026.

    JournalarXiv

  2. Greedy Rational Approximation for Frequency-Domain Model Reduction of Parametric LTI Systems

    F. Bělík, Y. Chen, and A. Narayan, 2025.

    arXiv

  3. Efficient and Robust Carathéodory-Steinitz Pruning of Positive Discrete Measures

    F. Bělík, J. Chan, and A. Narayan, 2025.

    arXiv

View all work on Google Scholar

Teaching

Courses and experience

Below are classes I have taught or assisted with.

MATH 1320

Engineering Calculus II

Instructor of Record · University of Utah · Spring 2026

Syllabus (PDF)

MATH 1310

Engineering Calculus I

Instructor of Record · University of Utah · Spring 2025

Syllabus (PDF)

MATH 6710

Applied Linear Operators and Spectral Methods

Teaching Assistant · University of Utah · Fall 2025

MATH 6610

Numerical Analysis I

Teaching Assistant · University of Utah · Spring 2024

MATH 4600

Mathematics in Medicine

Lab Instructor · University of Utah · Spring 2023

Syllabus (PDF)

Mathematics and Computer Science

Tutor, grader, and teaching assistant · Gustavus Adolphus College · 2019–2022

Resources

Course notes and reviews

Notes prepared during my graduate studies and shared as informal learning resources.

Background

Education

University of Utah
PhD Mathematics · 2022–present
Gustavus Adolphus College
BA Honors Mathematics and BA Computer Science · 2018–2022

Beyond mathematics

Other interests

Outside my studies, I enjoy running, hiking, tennis, biking, snowboarding, music, and board games. I also enjoy coding projects, particularly in Julia.

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