I joined the Department of Mathematical Sciences at Florida Tech in 2015 as an Assistant Professor in Applied Mathematics. My Ph.D. degree in Computational Engineering & Science was obtained under the supervision of Prof. Bartosz Protas, Dept. of Mathematics & Statistics at McMaster University, in 2012. After my graduation I spent three years as a Postdoctoral Research Fellow at the Department of Energy Resources Engineering at Stanford University working under the mentorship of co-directors of the Smart Fields Consortium Prof. Khalid Aziz and Prof. Louis J. Durlofsky.
My current scientific interests lie in, but are not limited to, the areas of applied mathematics focusing on combining theoretical and computational methods for problems in fluid dynamics, optimization and control theory. I have a strong background in applied mathematics involving PDEs, inverse problems and scientific computing as well as wide-ranging experience in working on interdisciplinary projects including industrial components.
I have openings for well-qualified students pursuing graduate, either master’s or doctoral, degrees in applied mathematics and operations research. I look for candidates with a strong background in applied mathematics, mathematical modelling, optimization as well as scientific computing. Please email me directly if you meet these criteria and would like to join my research group.
Ph.D., Computational Engineering and Science, McMaster University, Ontario, Canada, 2012
M.Sc., Computer Science (with distinction), Vitebsk State University, Belarus, 1999
B.Sc., Mathematics and Physics, Vitebsk State University, Belarus, 1997
2018 (Jun - Jul) | Visiting Assistant Professor (2 weeks), Dept. of Energy Resources Engineering, Stanford University, CA
2017 (Jun - Jul) | Visiting Assistant Professor (4 weeks), Dept. of Energy Resources Engineering, Stanford University, CA
2016 (Jul - Aug) | Visiting Assistant Professor (2 weeks), Dept. of Energy Resources Engineering, Stanford University, CA
2015 - 2016 | Visiting Assistant Professor in Applied Mathematics, Dept. of Mathematical Sciences, Florida Institute of Techology, FL
2012 - 2015 | Postdoctoral Research Fellow, Dept. of Energy Resources Engineering, Stanford University, CA. Project "Production and History Matching Optimization using Automatic Differentiation Techniques" (funded by Smart Fields Consortium, Stanford University)
2008 - 2012 | Research Assistant, Dept. of Mathematics & Statistics, McMaster University, Canada. Project "Computational Methods for the Optimal Reconstruction of Material Properties in Complex Multiphysics Systems" (in collaboration with General Motors of Canada)
2000 - 2002 | Research Assistant, Lykov Heat & Mass Transfer Institute, Minsk, Belarus. Project "The Physical and Mathematical Description of Processes of the Heat and Mass Transfers in Human Skin at Photodynamic Tumors Therapy" (grant of the Belarussian Fund of Fundamental Research)
- MTH 3220 - Honors PDE
- MTH 5051 - Applied Discrete Mathematics
- MTH 6300 - Topics in Numerical and Computational Mathematics: Numerical Optimizations
- MTH 5051 - Applied Discrete Mathematics
- MTH 5107 / ORP 5010 - Optimization Models and Methods / Mathematical Programming
- MTH 5007 / ORP 5001 - Introduction to Optimization / Deterministic OR Models
- MTH 3210 - Introduction to PDEs & Applications
- MTH 3200 - Honors Differential Equations
- MTH 3107 - Optimization
- MTH 2201 / 2202 - Differential Equations / Linear Algebra
- MTH 2001 - Calculus 3
Refereed Journal Publications
- Arbic P.R., Bukshtynov V. On Reconstruction of Biomedical Images by Efficient Sample-based Parameterization (in press).
- Koolman P. M., Bukshtynov V. A Multiscale Optimization Framework for Biomedical Applications through Multilevel PCA-based Control Space Reduction, Biomedical Physics & Engineering Express, 7(2) (2021), 025005.
- Abdulla U. G., Bukshtynov V., Seif S. Cancer Detection through Electrical Impedance Tomography and Optimal Control Theory: Theoretical and Computational Analysis, Mathematical Biosciences & Engineering, 18(4) (2021), 4834-4859.
- Abdulla U. G., Bukshtynov V., Hagverdiyev A. Gradient Method in Hilbert‑Besov Spaces for the Optimal Control of Parabolic Free Boundary Problems, Journal of Computational and Applied Mathematics 346 (2019), 84-109.
- Volkov O., Bukshtynov V., Durlofsky L.J. and Aziz K. Gradient-based Pareto Optimal History Matching for Noisy Data of Multiple Types, Computational Geosciences 22(6) (2018), 1465-1485.
- Bukshtynov V., Volkov O., Durlofsky L.J. and Aziz K. Comprehensive Framework for Gradient-based Optimization in Closed-Loop Reservoir Management, Computational Geosciences 19(4) (2015), 877-897.
- Bukshtynov V., Protas B. Optimal Reconstruction of Material Properties in Complex Multiphysics Phenomena, Journal of Computational Physics 242 (2013), 889-914.
- Bukshtynov V., Volkov O., Protas B. On Optimal Reconstruction of Constitutive Relations, Physica D: Nonlinear Phenomena 240 (2011), 1228-1244.
- Shulman Z., Makhanek A., Bukshtynov V., Gubarev S. Statement of Thermophysical Problems of Photodynamic Tumors Therapy, Heat & Mass Transfer – 2001 (National Academy of Science, Belarus) (2002), 122–128 (in Russian).
- Computational Methods for the Optimal Reconstruction of Material Properties in Complex Multiphysics Systems, Ph.D. Dissertation, McMaster University, Open Access Dissertation and Theses. Paper 6795. http://hdl.handle.net/11375/11859, (2012)
- Two-sided Error Estimations in the Courses Numerical Methods and Modeling, M.Sc. Thesis, Vitebsk State University (1999)
- Bukshtynov V., Polyak E. Higher Mathematics, Vitebsk State Medical University Text-book (Calculus with elements of Mathematical Statistics) for the 2nd year students of Pharmaceutical Dept, with instructions and assignment problems, 100pp. (2002, 2012)
Research and Technical Reports
- Bukshtynov V. Optimization Framework of EIT-OPT. Department of Mathematical Sciences, Florida Institute of Technology (2020)
- Volkov O., Kourounis D., Bukshtynov V. Optimization Module of AD-GPRS. Department of Energy Reservoirs Engineering, SUPRI-B, Stanford University (2014)
- Voskov D., Zaydullin R., Garipov T., Iskhakov R., Zhou Y., Volkov O., Kourounis D., Semenova A., Bukshtynov V. Reservoir Simulator AD-GPRS. User Manual, version 1.0. Department of Energy Reservoirs Engineering, SUPRI-B, Stanford University (2013)
- Atena A., Yapalparvi R., Bukshtynov V., Protas B. Optimization and Parameter Estimation in MIG Welding – Multi-Objective Framework and Modelling Mass Transfer with Effective Surfaces, Report #4 for a Collaborative Research Project with GM (2011)
- Atena A., Yapalparvi R., Bukshtynov V., Volkov O., Protas B. Optimization and Parameter Estimation in MIG Welding – Towards Multi-Objective Framework and Modelling Mass Transfer with Effective Surfaces, Report #3 for a Collaborative Research Project with GM (2010)
- Volkov O., Yapalparvi R., Bukshtynov V., Protas B. Modelling, Optimization and Estimation of the Systems Involving Interaction with Plasma Column, Report #2 for a Collaborative Research Project with GM (2009)
- Volkov O., Bukshtynov V., Protas B. A Unified Approach to Solving Free-Boundary and Inverse Problems for a Stationary Weld Pool, with Some Notes on the Related Problem of Parameter Estimation, Report #1 for a Collaborative Research Project with GM (2008)
- Makhanek A. et al. The Physical and Mathematical Description of Processes of Heat and Mass Transfer in Human Skin During Photodynamic Therapy of Tumours, Report #4 for Luikov Heat and Mass Transfer Institute, National Academy of Science, Belarus (2002
Recognition & Awards
2019 | NSF/ICERM Travel Award to attend 2019 ICERM Topical Workshop, Brown University, RI
2018 | NSF/ICERM Travel Award to attend 2018 ICERM Topical Workshop, Brown University, RI
2018 | Mobility Program Award to attend 2018 IWR School, Heidelberg University, Germany
2018 | NSF/CBMS Travel Award to attend 2018 NSF-CBMS, Jackson State University, MS
2017 | NSF/SIAM Early Career Travel Award to attend SIAM GS17, Erlangen, Germany
2017 | NSF/AMS Travel Award to attend MCA 2017, Montreal, Canada
2012-2015 | Smart Fields Consortium Postdoctoral Research Fellowship. Energy Resources Engineering Dept., Stanford University
2013 | The 2012 Cecil Graham Doctoral Dissertation Award. Canadian Applied and Industrial Mathematics Society (CAIMS)
2011 | Applied Mathematics Perspectives (AMP 2011) Poster Competition - Second Prize. Canadian Applied and Industrial Mathematics Society (CAIMS)
2011 | Ontario Graduate Scholarship (OGS). Ministry of Training, Colleges and Universities, Ontario, Canada
2010 | Ontario Graduate Scholarship (OGS). Ministry of Training, Colleges and Universities, Ontario, Cana
Current and Past Research Directions:
- Optimal Reconstruction of Constitutive Relations for Porous Media Flows
- Inverse Problem of Cancer Detection Through Electrical Impedance Tomography (EIT)
- Computational Optimization Framework for EIT
- Optimal Control of Parabolic Free Boundary Problems
- Pareto Optimal History Matching for Noisy Data of Multiple Types
- Gradient-based Closed-Loop Reservoir Modeling (CLRM)
- Modeling Proxy Time-Lapse 4D Seismic Observations
- Efficient Control Space Parameterization
- Gradient-based History Matching (HM) Optimization
- Optimal Reconstruction of Material Properties in Complex Multiphysics Phenomena
- Paul Arbic - M.S. thesis "Optimization Framework for Reconstructing Biomedical Images by Efficient Sample-based Parameterization" (2020, Operations Research)
- Priscilla Koolman - undergraduate research student (2019-2020), BS Biomedical Engineering & Computational Mathematics (minor)