Stochastic Differential Equations · Data Assimilation · Spatial Statistics
Hamza Ruzayqat

Hamza Ruzayqat

Research Scientist, King Abdullah University of Science and Technology (KAUST)

I design and analyse Monte Carlo and stochastic algorithms that turn noisy, partial observations of complex systems into reliable inference with quantified uncertainty. My work centres on three connected themes:

  • Inference for stochastic differential equations: unbiased and multilevel estimators, and fast learning of both the drift and diffusion terms of SDEs from noisy partial data (WAIVES, forthcoming).
  • Data assimilation: sequential MCMC, localization and lagged particle filters for high-dimensional, nonlinear, non-Gaussian geophysical models.
  • Spatial statistics: Whittle–Matérn random fields with spatially varying smoothness, with efficient sampling in one and two dimensions.
Explore my research Publications Google Scholar GitHub
Local Sequential MCMC assimilating real drifter and SWOT satellite observations of the North Atlantic (Aug 2024).
16+3articles in top numerical & applied mathematics journals + preprints
42invited & conference talks
16international collaborators
8open-source research codes
About

Hello!

I am a Research Scientist at KAUST (CEMSE Division), where I previously held a postdoctoral position (2019–2022). My work sits at the intersection of computational statistics, stochastic analysis and geophysical modelling.

I collaborate with groups at Imperial College London, UCL, INRIA, the University of Colorado Boulder, Florida State University and KAUST, and I release open-source implementations of my methods.

  • PhD & M.S. in Mathematics — University of Tennessee, Knoxville, 2019
  • B.S. in Physics & Mathematics — Birzeit University, Palestine, 2012

Recent news

  • UpcomingPresenting at the 31st Conference on Integrated Observing and Assimilation Systems for the Atmosphere, Oceans, and Land Surface (IOAS-AOLS), AMS Annual Meeting, Denver, CO (Jan 10–14, 2027).
  • UpcomingCo-organizing (with Vanja Dukic) a minisymposium on Inference in Stochastic Differential Equations at CFE-CMStatistics 2026, HTW Berlin (Dec 12–14, 2026). Conference
  • Accepted"Two Localization Strategies for Sequential MCMC Data Assimilation with Applications to Nonlinear Non-Gaussian Geophysical Models" to appear in the Journal of Advances in Modeling Earth Systems (JAMES). arXiv
  • SeminarDepartment of Applied Mathematics (APPM), University of Colorado Boulder: learning SDEs from noisy partial data.
  • Invited54th Barrett Lectures, University of Tennessee, Knoxville. Event
  • PreprintTwo Localization Strategies for Sequential MCMC Data Assimilation. arXiv:2603.05817
  • PreprintWhittle–Matérn Fields with Variable Smoothness. arXiv:2602.16581
  • WorkshopKAUST 2025 Workshop on Statistics: Whittle–Matérn fields with variable smoothness. Event
  • ConferenceSpeaker and session organizer (Bayesian Inference), MCM 2025, Illinois Institute of Technology, Chicago. Event
Older news
  • ConferenceISDA-Online: Open Session on Non-linear Data Assimilation. Event
  • Conference9th International Arab Conference on Mathematics and Computations, Zarqa University, Jordan. Event
  • ConferenceSpeaker and minisymposium organizer (Data Assimilation), SIAM CSE25, Fort Worth, TX. Session
  • SeminarDepartment of Mathematics, Texas A&M University.
  • ColloquiumDepartment of Scientific Computing, Florida State University.
  • ConferenceICMS25, American University of Sharjah, UAE.
  • SeminarUQ Seminar, RWTH Aachen University, Germany (hybrid).
  • Conference14th AIMS Conference on Dynamical Systems, NYU Abu Dhabi; MathConnect 2024, KFUPM.
  • PreprintLocal Sequential MCMC for Data Assimilation with Applications in Geoscience. arXiv:2409.07111
  • SeminarDepartment of Statistics and Data Science, Washington University in St. Louis.
  • InvitedISE Department, University of Illinois Urbana-Champaign.
Research

Research highlights

Selected results across my research: inference for stochastic differential equations, data assimilation, spatial statistics and Bayesian inverse problems. The common thread is stochastic algorithms with provable properties, such as convergence, unbiasedness or stability with respect to dimension, that remain computationally practical for realistic models.

North Atlantic sea-surface height, velocity and temperature reconstructed by localized sequential MCMC versus HYCOM reanalysis
Real-data experiment (JAMES, to appear): localized sequential MCMC assimilates real drifter velocity and temperature observations and SWOT sea-surface height into a three-layer shallow-water model of the North Atlantic (state dimension 67,200) over 240 cycles, starting from the HYCOM state at the initial time with added noise. Columns: analysis at the first cycle (left) and final cycle (centre), and the HYCOM reanalysis at the final time (right). Rows: sea-surface height, eastward and northward velocity, temperature.
Data assimilation

Sequential MCMC for high-dimensional geophysical filtering

Ensemble Kalman methods are fast but rely on linear–Gaussian approximations, while standard particle filters suffer from weight degeneracy in high dimensions. Sequential MCMC avoids importance weights altogether and is provably convergent. My localized variants restrict the MCMC updates to observed regions, reducing the effective dimension, and have been applied to nonlinear, non-Gaussian models with 104–105 state variables.

Sequential MCMCLocalization Particle filtersOcean models

JAMES (to appear, 2026) · Q. J. R. Meteorol. Soc. (2024) · SIAM/ASA JUQ (2022)

Two localization strategies

Localization for sequential MCMC

Two localized versions of sequential MCMC: one updates all observed blocks jointly with parallel chains, the other updates each observed block independently with a halo around it. For linear–Gaussian observations the analysis can be sampled exactly.

JAMES, to appear

Shallow-water height fields: signal vs lagged particle filter vs ensemble Kalman filters

Lagged particle filtering

A lag approximation whose bias is controlled uniformly in the dimension. Pictured: shallow-water height; averaged over 50 runs, the LPF with 100 particles stays closer to the true signal than EnKF, ETKF and square-root ETKF with 1000 ensemble members.

SIAM/ASA J. Uncertain. Quantif.

Ocean velocity and height fields estimated from drifter observations

Lagrangian data assimilation

Sequential MCMC for filtering from drifting observers, including a real-data case with 12 NOAA drifters whose locations are treated as unknown. Pictured: true signal, filter mean and error for a shallow-water model with known drifter locations.

Q. J. R. Meteorol. Soc., 2024

3D surface of the estimated log-permeability field from the unbiased Schrödinger–Föllmer sampler

Unbiased & multilevel Monte Carlo

The Schrödinger–Föllmer sampler draws from a target distribution by simulating a diffusion bridge that starts at zero and ends, at time one, distributed exactly as the target. Our randomized estimators remove both its time-discretization bias and the bias from approximating its drift. Pictured: the estimated log-permeability field of an elliptic PDE inverse problem (3D view).

J. Comput. Phys., 2023 · SIAM J. Sci. Comput., 2023

Bayesian anomaly detection

Bayesian inverse problems

Recovering the location, shape, fractional order and diffusivity of hidden anomalies in variable-order fractional media from noisy measurements.

Preprint, 2025

Sample covariance surfaces of Whittle–Matérn fields with spatially varying smoothness

Spatial statistics: variable smoothness

Whittle–Matérn random fields whose smoothness varies over space, so a single Gaussian model can be rough in some regions and smooth in others.

Preprint, 2026

Publications

Papers & preprints

In SIAM journals, J. Comput. Phys., QJRMS, Mathematics of Computation, JAMES, Statistics and Computing, and others.

Journal articles

  • 2026
    Two Localization Strategies for Sequential MCMC Data Assimilation with Applications to Nonlinear Non-Gaussian Geophysical Models Ruzayqat, H., Chipilski, H. G. & Knio, O. Journal of Advances in Modeling Earth Systems (JAMES), to appear
    PDF
  • 2026
    On Time Uniform Wong–Zakai Approximation Theorems Del Moral, P., Hu, S., Jasra, A., Ruzayqat, H. & Wang, X. Mathematics of Computation, 95 (2026), 2481–2514
    PDF
  • 2024
    Bayesian Parameter Inference for Partially Observed Diffusions using Multilevel Stochastic Runge–Kutta Methods Del Moral, P., Hu, S., Jasra, A., Ruzayqat, H. & Wang, X. International Journal for Uncertainty Quantification, 15(2), 1–18
    PDF
  • 2024
    Unbiased and Multilevel Methods for a Class of Diffusions Partially Observed via Marked Point Processes Alvarez, M., Jasra, A. & Ruzayqat, H. Statistics and Computing, 34(198)
    PDF
  • 2024
    Unbiased Parameter Estimation for Partially Observed Diffusions Awadelkarim, E., Jasra, A. & Ruzayqat, H. SIAM Journal on Control and Optimization, 62(5), 2664–2694
    PDF
  • 2024
    Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations Ruzayqat, H., Beskos, A., Crisan, D., Jasra, A. & Kantas, N. Quarterly Journal of the Royal Meteorological Society, 150(761), 2418–2439
    PDF
  • 2023
    Bayesian Parameter Inference for Partially Observed Stochastic Volterra Equations Jasra, A., Ruzayqat, H. & Wu, A. Statistics and Computing, 34(2), 1–12
    PDF
  • 2023
    Unbiased Estimation using Underdamped Langevin Dynamics Ruzayqat, H., Chada, N. K. & Jasra, A. SIAM Journal on Scientific Computing, 45(6), A3047–A3070
    PDF
  • 2023
    Unbiased Estimation using a Class of Diffusion Processes Ruzayqat, H., Beskos, A., Crisan, D., Jasra, A. & Kantas, N. Journal of Computational Physics, 472, 111643
    PDF
  • 2022
    Log-Normalization Constant Estimation using the Ensemble Kalman–Bucy Filter with Application to High-Dimensional Models Crisan, D., Del Moral, P., Jasra, A. & Ruzayqat, H. Advances in Applied Probability, 54(4), 1139–1163
    PDF
  • 2022
    Unbiased Parameter Inference for a Class of Partially Observed Lévy-Process Models Ruzayqat, H. & Jasra, A. Foundations of Data Science, 4(2), 299–322
    PDF
  • 2022
    A Lagged Particle Filter for Stable Filtering of Certain High-Dimensional State-Space Models Ruzayqat, H., Er-Raiy, A., Beskos, A., Crisan, D., Jasra, A. & Kantas, N. SIAM/ASA Journal on Uncertainty Quantification, 10(3), 1130–1161
    PDF
  • 2022
    Multilevel Estimation of Normalization Constants Using the Ensemble Kalman–Bucy Filter Ruzayqat, H., Chada, N. K. & Jasra, A. Statistics and Computing, 32(38)
    PDF
  • 2021
    Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models Beskos, A., Crisan, D., Jasra, A., Kantas, N. & Ruzayqat, H. SIAM Journal on Scientific Computing, 43(4), A2555–A2580
    PDF
  • 2020
    Unbiased Estimation of the Solution to Zakai's Equation Ruzayqat, H. & Jasra, A. Monte Carlo Methods and Applications, 26(2), 113–129
    PDF
  • 2018
    A Rejection Scheme for Off-Lattice Kinetic Monte Carlo Simulation Ruzayqat, H. M. & Schulze, T. P. Journal of Chemical Theory and Computation, 14(1), 48–54
    PDF

Preprints

  • 2026
    Whittle–Matérn Fields with Variable Smoothness Ruzayqat, H., Lei, W., Bolin, D., Turkiyyah, G. & Knio, O.
    PDF
  • 2025
    Bayesian Anomaly Detection in Variable-Order and Variable-Diffusivity Fractional Mediums Ruzayqat, H., Turkiyyah, G. & Knio, O.
  • 2024
    Local Sequential MCMC for Data Assimilation with Applications in Geoscience Ruzayqat, H. & Knio, O.
    PDF

Dissertation & technical reports

  • 2022
    Development of Image Processing Algorithm for an Atomic Force Microscopy Scanner Ashby, P., Bhatt, G., Baroi, M., Kao, C.-Y., Kramer, P. R., Kivela, M., Lakoba, T., Matz, S. & Ruzayqat, H. Mathematics in Industry Reports, Cambridge University Press
    PDF
  • 2019
    Rejection Enhanced Off-Lattice Kinetic Monte Carlo Ruzayqat, H. M. Doctoral dissertation, University of Tennessee
    PDF
  • 2017
    Temperature Effects in Reacting Porous Media Applications Allaire, H., Odu, A. G., Gu, B., Lu, W., Newell, A., Paranamana, J., Phan, T. & Ruzayqat, H. GSMMC 2017 Summer Camp

Selected journals (SCImago) with SJR index

Journal of Advances in Modeling Earth Systems — SCImago Journal & Country Rank SIAM Journal on Scientific Computing Journal of Computational Physics Quarterly Journal of the Royal Meteorological Society Journal of Chemical Theory and Computation SIAM Journal on Control and Optimization Mathematics of Computation SIAM/ASA Journal on Uncertainty Quantification Statistics and Computing
Software

Open-source code

Reproducible implementations accompanying my papers.

Local Sequential MCMC for Data Assimilation Sequential MCMC for Lagrangian Data Assimilation Lagged Particle Filter for High-Dimensional Models Unbiased Estimation with Underdamped Langevin Dynamics Unbiased Estimation with a Class of Diffusion Processes Log-Normalizing Constant Estimation with EnKBF Multilevel EnKBF Normalizing Constants Score-Based Parameter Estimation
Network

Collaborators

 

Talks

Invited & conference talks

42 talks at universities and international meetings across the US, Europe and the Middle East.

DateEventLocation
Jan 2027UpcomingConference31st Conference on Integrated Observing and Assimilation Systems for the Atmosphere, Oceans, and Land Surface (IOAS-AOLS), AMS Annual MeetingDenver, CO, USA
Dec 2026UpcomingConferenceCFE-CMStatistics 2026, co-organizer (with Vanja Dukic) of the session on Inference in Stochastic Differential EquationsBerlin, Germany
May 2026SeminarDepartment of Applied Mathematics (APPM), University of Colorado Boulder: Learning SDEs from noisy partial dataBoulder, CO, USA
May 2026InvitedConference54th Barrett Lectures, University of TennesseeKnoxville, TN, USA
Nov 2025WorkshopKAUST 2025 Workshop on Statistics: Whittle–Matérn fields with variable smoothnessThuwal, Saudi Arabia
Jul 2025ConferenceInternational Conference on Monte Carlo Methods and Applications (MCM 2025), speaker and session organizerChicago, IL, USA
May 2025ConferenceISDA-Online: Open Session on Non-linear Data AssimilationOnline
May 2025Conference9th International Arab Conference on Mathematics and Computations, Zarqa UniversityZarqa, Jordan
Mar 2025ConferenceSIAM CSE25, speaker and minisymposium organizer on Data AssimilationFort Worth, TX, USA
Feb 2025SeminarDepartment of Mathematics, Texas A&M UniversityCollege Station, TX, USA
Feb 2025ColloquiumDepartment of Scientific Computing, Florida State UniversityTallahassee, FL, USA
Feb 2025ConferenceFourth International Conference on Mathematics and Statistics (ICMS25), American University of SharjahSharjah, UAE
Feb 2025SeminarUQ Seminar, RWTH Aachen University (hybrid)Aachen, Germany
Show all earlier talks
Dec 2024Conference14th AIMS Conference on Dynamical Systems, Differential Equations and Applications, NYU Abu DhabiAbu Dhabi, UAE
Dec 2024ConferenceMathConnect 2024: International Conference on Mathematics and its Applications, KFUPMDhahran, Saudi Arabia
Sep 2024ConferenceISDA-Online: Open Session on Data AssimilationOnline
Mar 2024SeminarDepartment of Statistics and Data Science, Washington University in St. LouisSt. Louis, MO, USA
Jan 2024InvitedSeminarISE Department, University of Illinois Urbana-ChampaignUrbana, IL, USA
Oct 2023ConferenceInternational Symposium on Data Assimilation (ISDA)Bologna, Italy
Sep 2023InvitedSeminarStochastic Seminar, New York University Abu DhabiAbu Dhabi, UAE
Jun 2023InvitedWorkshop24th STUOD Sandbox Workshop on Data Assimilation, Imperial College LondonLondon, UK
Jan 2023ConferenceJoint Mathematics Meetings (JMM 2023)Boston, MA, USA
Nov 2022InvitedSeminarApplied Mathematics and Computational Sciences, CEMSE, KAUSTThuwal, Saudi Arabia
Sep 2022SeminarDepartment of Statistics, Imperial College LondonLondon, UK
Sep 2022Workshop3rd Stochastic Transport in Upper Ocean Dynamics Annual Workshop, Imperial College LondonLondon, UK
Jul 2022Conference7th Palestinian Conference on Modern Trends in Mathematics, Birzeit UniversityBirzeit, Palestine
Jul 2022Conference15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods (MCQMC)Linz, Austria
Jun 2022ConferenceIMS Annual Meeting in Probability and StatisticsLondon, UK
Jun 2022WorkshopEnsemble Kalman Filter (EnKF) WorkshopBalestrand, Norway
Apr 2022InvitedSeminarSeminar on Data Science, University of TennesseeKnoxville, TN, USA
Apr 2022ConferenceSIAM Conference on Uncertainty Quantification (UQ22)Atlanta, GA, USA
Dec 2021InvitedSeminarGraduate Seminar, KAUST (virtual)Thuwal, Saudi Arabia
Nov 2021Guest lectureGuest Lecturer, KAUSTThuwal, Saudi Arabia
Nov 2021InvitedSeminarSeminar on Optimization and Machine Learning, New Jersey Institute of Technology (virtual)Newark, NJ, USA
Aug 2021Conference13th International Conference on Monte Carlo Methods and Applications, University of Mannheim (virtual)Mannheim, Germany
Mar 2019InvitedSeminarDepartment of Mathematics, Colorado State UniversityFort Collins, CO, USA
Oct 2018SeminarSeminar on Numerical Mathematics, University of TennesseeKnoxville, TN, USA
Oct 2018InvitedSeminarDepartment of Materials Science and Engineering, University of TennesseeKnoxville, TN, USA
Jul 2018ConferenceSIAM Conference on Mathematical Aspects of Materials SciencePortland, OR, USA
Jun 2018WorkshopMathematical Problems in Industry Workshop, Claremont Center for the Mathematical SciencesClaremont, CA, USA
Feb 2018SeminarSeminar on Numerical Mathematics, University of TennesseeKnoxville, TN, USA
Sep 2017SeminarSeminar on Numerical Mathematics, University of TennesseeKnoxville, TN, USA
Jun 2017WorkshopGSMMC 2017 Summer Camp, Rensselaer Polytechnic InstituteTroy, NY, USA
Nov 2016SeminarSeminar on Numerical Mathematics, University of TennesseeKnoxville, TN, USA
Teaching

Courses taught

Instructor of record and teaching assistant for undergraduate mathematics courses.

TermCourseRoleInstitution
Fall 2018Calculus IInstructor (2 sections)University of Tennessee, Knoxville
Spring 2016Calculus IIInstructor (2 sections)University of Tennessee, Knoxville
Fall 2015College AlgebraInstructor (2 sections)University of Tennessee, Knoxville
2014–2016Basic Calculus, College Algebra, Calculus IITeaching assistant (10 sections)University of Tennessee, Knoxville
Spring 2013College Algebra; Complex NumbersInstructor (3 sections)Palestine Polytechnic University, Hebron
Contact

Get in touch

Email

hamza.ruzayqat@kaust.edu.sa

Address

King Abdullah University of Science and Technology
Thuwal 23955, Saudi Arabia

Online

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