Research Interests

My current research focuses on studying an algorithm for data assimilation applied to equations of fluid dynamics. I am also interested in numerical schemes used to simulate PDEs, particularly for turbulent fluids. I’m also interested in application of data assimilation, particularly in geophysics. Machine learning algorithms, particularly physics informed neural networks have been a more recent interest of mine.

  • Partial Differential Equations
  • Computational Fluid Dynamics
  • Numerical Analysis
  • Data Assimilation
    • Applications in geophysics
  • Physics Informed Neural Networks

Publications

  • E. S. Titi and C. Victor.
    On the Inadequacy of Nudging Data Assimilation Algorithms for Non-Dissipative Systems.
    Discrete and Continuous Dynamical Systems – Series S (accepted, 2025).

  • N. Ning and C. Victor.
    An Assessment of Ensemble Kalman Filter and Azouani–Olson–Titi Algorithms for Data Assimilation: A Comparative Study.
    Communications in Computational Physics (accepted, 2025).

  • A. Larios and C. Victor.
    Continuous data assimilation for the 3D and higher-dimensional Navier–Stokes equations with higher-order fractional diffusion.
    Journal of Mathematical Analysis and Applications, 540 (1), 128644 (2024).

  • A. Larios, M. Petersen, and C. Victor.
    Application of Continuous Data Assimilation in High-Resolution Ocean Modeling.
    Communications in Computational Physics, 35 (5), 1418–1444 (2024).

  • T. Franz, A. Larios, and C. Victor.
    The bleeps, the sweeps, and the creeps: Convergence rates for dynamic observer patterns via data assimilation for the 2D Navier–Stokes equations.
    Computer Methods in Applied Mechanics and Engineering, 392, 114673 (2022).

  • D. Foster, B. Frost-LaPlante, J. Restrepo, and C. Victor.
    Gradient Sensing via Cell Communication.
    Physical Review E, 103 (2), 022405 (2021).

  • A. Larios and C. Victor.
    Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study.
    Communications in Computational Physics, 29, 1273–1298 (2021).

Preprints

  • E. Carlson, A. Farhat, V. R. Martinez, and C. Victor.
    On the Infinite-Nudging Limit of the Nudging Filter for Continuous Data Assimilation.
    arXiv:2408.02646 (2024). (Submitted)

  • E. Carlson, A. Farhat, V. R. Martinez, and C. Victor.
    Determining Modes, Synchronization, and Intertwinement.
    arXiv:2408.01064 (2024). (Submitted)

  • A. Larios, Y. Pei, and C. Victor.
    The second-best way to do sparse-in-time continuous data assimilation: Improving convergence rates for the 2D and 3D Navier–Stokes equations.
    arXiv:2303.03495 (2023). (Submitted)

  • Z. Pan, O. Reshetar, and C. Victor.
    Optimal Sensor Placement and Movement in Data Assimilation.
    (In progress, 2025)

  • A. Farhat, E. S. Titi, and C. Victor.
    A Critical Report on Back-and-Forth Data Assimilation Nudging Algorithms.
    (In progress, 2025)