< Back to home page

Research Interests

Grants

  1. National Science Foundation DMS-2309197 ($268K, 07/15/2023 - 06/30/2026)
    Project title: "Tensorial Reduced Order Models: Development, Analysis, and Applications" (PI)
  2. Office of Naval Research N00014-21-1-2370 ($136K out of $377K total, 04/29/2021 - 04/28/2024)
    Project title: "Data driven reduced order models for inverse problems in heterogeneous media" (Co-PI)
  3. Office of Naval Research N00014-17-1-2057 ($126K out of $299K total, 01/01/2017 - 12/31/2020)
    Project title: "A computational and theoretical study of forward and inverse scattering in
    heterogeneous media"     (Co-PI)
  4. National Science Foundation DMS-1619821 ($209K, 06/15/2016 - 05/31/2020)
    Project title: "Reduced order models for imaging and inversion with waves and diffusive fields" (PI)
  5. University of Houston New Faculty Research Program ($6K, 01/08/2016 - 08/31/2016)
    Project title: "Reduced order models for medical ultrasound imaging" (PI)

Journal Publications

  1. When data driven reduced order modeling meets full waveform inversion.
    L. Borcea, J. Garnier, A.V. Mamonov, J. Zimmerling, SIAM Review 66(3):10.1137/23M1552826, 2024.
    DOI: 10.1137/23M1552826, Preprint: arXiv:2302.05988 [math.NA]
  2. Tensorial parametric model order reduction of nonlinear dynamical systems.
    A.V. Mamonov, M.A. Olshanskii, SIAM Journal on Scientific Computing 46(3):10.1137/23M1553789, 2024.
    DOI: 10.1137/23M1553789, Preprint: arXiv:2302.08490 [math.NA]
  3. Waveform inversion via reduced order modeling.
    L. Borcea, J. Garnier, A.V. Mamonov, J. Zimmerling, Geophysics, 88(2):R175-R191, 2023.
    DOI: 10.1190/geo2022-0070.1, Preprint: arXiv:2202.01824 [math.NA]
  4. Waveform inversion with a data driven estimate of the internal wave.
    L. Borcea, J. Garnier, A.V. Mamonov, J. Zimmerling, SIAM Journal on Imaging Sciences, 16(1):280-312, 2023.
    DOI: 10.1137/22M1517342, Preprint: arXiv:2208.11051 [math.NA]
  5. Interpolatory tensorial reduced order models for parametric dynamical systems.
    A.V. Mamonov, M.A. Olshanskii, Computer Methods in Applied Mechanics and Engineering, 397:115122, 2022.
    DOI: 10.1016/j.cma.2022.115122, Preprint: arXiv:2111.00649 [math.NA]
  6. Distance Preserving Model Order Reduction of Graph-Laplacians and Cluster Analysis.
    V. Druskin, A.V. Mamonov, M. Zaslavsky, Journal of Scientific Computing, 90:32, 2022.
    DOI: 10.1007/s10915-021-01660-3, Preprint: arXiv:1809.03048 [cs.LG]
  7. Reduced order model approach for imaging with waves.
    L. Borcea, J. Garnier, A.V. Mamonov, J. Zimmerling, Inverse Problems, 38(2):025004, 2022.
    DOI: 10.1088/1361-6420/ac41d0, Preprint: arXiv:2108.01609 [math.NA]
  8. Reduced Order Model Approach to Inverse Scattering.
    L. Borcea, V. Druskin, A.V. Mamonov, M. Zaslavsky, J. Zimmerling, SIAM Journal on Imaging Sciences 13(2):685-723, 2020.
    DOI: 10.1137/19M1296355, Preprint: arXiv:1910.13014 [math.NA]
  9. Reduced order models for spectral domain inversion: Embedding into the continuous problem and generation of internal data.
    L. Borcea, V. Druskin, A.V. Mamonov, S. Moskow, M. Zaslavsky, Inverse Problems 36(5):055010, 2020.
    DOI: 10.1088/1361-6420/ab750b, Preprint: arXiv:1909.06460 [math.NA]
  10. Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models.
    L. Borcea, V. Druskin, A.V. Mamonov, M. Zaslavsky, Journal of Computational Physics 381:1-26, 2019.
    DOI: 10.1016/j.jcp.2018.12.021, Preprint: arXiv:1805.03747 [math.NA]
  11. Polyp detection with computer-aided diagnosis in white light colonoscopy: comparison of three different methods.
    P.N. Figueiredo, I.N. Figueiredo, L. Pinto, S. Kumar, Y.-H. R. Tsai, A.V. Mamonov,
    Endoscopy International Open 07(02):E209-E215, 2019.
    DOI: 10.1055/a-0808-4456
  12. Untangling the nonlinearity in inverse scattering with data-driven reduced order models.
    L. Borcea, V. Druskin, A.V. Mamonov, M. Zaslavsky, Inverse Problems 34(6):065008, 2018.
    DOI: 10.1088/1361-6420/aabb16, Preprint: arXiv:1704.08375 [math.NA]
  13. A nonlinear method for imaging with acoustic waves via reduced order model backprojection.
    V. Druskin, A.V. Mamonov, M. Zaslavsky, SIAM Journal on Imaging Sciences, 11(1):164-196, 2018.
    DOI: 10.1137/17M1133580, Preprint: arXiv:1704.06974 [math.NA]
  14. A discrete Liouville identity for numerical reconstruction of Schrödinger potentials.
    L. Borcea, F. Guevara Vasquez, A.V. Mamonov, Inverse Problems and Imaging 11(4):623-641, 2017.
    DOI: 10.3934/ipi.2017029, Preprint: arXiv:1601.07603 [math.NA]
  15. Second-Harmonic Imaging in Random Media.
    L. Borcea, W. Li, A.V. Mamonov, J.C. Schotland, Inverse Problems 33(6):065004, 2017.
    DOI: 10.1088/1361-6420/aa6ab1, Preprint: arXiv:1611.02774 [math.NA]
    Selected for Inverse Problems 2017 Highlights Collection
  16. Multi-scale S-fraction reduced-order models for massive wavefield simulations.
    V. Druskin, A.V. Mamonov, M. Zaslavsky, Multiscale Modeling and Simulation 15(1):445-475, 2017.
    DOI: 10.1137/16M1072103, Preprint: arXiv:1604.06750 [math.NA]
  17. Direct, nonlinear inversion algorithm for hyperbolic problems via projection-based model reduction.
    V. Druskin, A.V. Mamonov, A.E. Thaler and M. Zaslavsky, SIAM Journal on Imaging Sciences 9(2):684-747, 2016.
    DOI: 10.1137/15M1039432, Preprint: arXiv:1509.06603 [math.NA]
  18. A model reduction approach to numerical inversion for a parabolic partial differential equation.
    L. Borcea, V. Druskin, A.V. Mamonov and M. Zaslavsky, Inverse Problems 30(12):125011, 2014.
    DOI: 10.1088/0266-5611/30/12/125011, Preprint: arXiv:1210.1257 [math.NA]
  19. Automated polyp detection in colon capsule endoscopy.
    A.V. Mamonov, I.N. Figueiredo, P.N. Figueiredo, Y.-H. R. Tsai, IEEE Transactions on Medical Imaging, 33(7):1488-1502, 2014.
    DOI: 10.1109/TMI.2014.2314959, Preprint: arXiv:1305.1912 [cs.CV]
    Featured by the MIT Technology Review, BioNews Texas and Vision Systems Design.
  20. Quantitative photoacoustic imaging in radiative transport regime.
    A.V. Mamonov and K. Ren, Communications in Mathematical Sciences, 12(2):201-234, 2014.
    DOI: 10.4310/CMS.2014.v12.n2.a1, Preprint: arXiv:1207.4664 [math.NA]
  21. Study of noise effects in electrical impedance tomography with resistor networks.
    L. Borcea, F. Guevara Vasquez and A.V. Mamonov, Inverse Problems and Imaging, 7(2):417-443, 2013.
    DOI: 10.3934/ipi.2013.7.417, Preprint: arXiv:1105.1183 [math-ph]
  22. Point source identification in non-linear advection-diffusion-reaction systems.
    A.V. Mamonov and Y.-H. R. Tsai, Inverse Problems 29(3):035009, 2013.
    DOI: 10.1088/0266-5611/29/3/035009, Preprint: arXiv:1202.2373 [math-ph]
  23. Pyramidal resistor networks for electrical impedance tomography with partial boundary measurements.
    L. Borcea, V. Druskin, A.V. Mamonov and F. Guevara Vasquez, Inverse Problems 26(10):105009, 2010.
    DOI: 10.1088/0266-5611/26/10/105009, PDF: pyramidal.pdf
  24. Circular resistor networks for electrical impedance tomography with partial boundary measurements.
    L. Borcea, V. Druskin and A.V. Mamonov, Inverse Problems 26(4):045010, 2010, IOPselect article.
    DOI: 10.1088/0266-5611/26/4/045010, PDF: circular.pdf

Refereed Proceedings

  1. Velocity estimation via model order reduction.
    A.V. Mamonov, L. Borcea, J. Garnier, J. Zimmerling, Second International Meeting for Applied Geoscience & Energy, pp. 752-756, 2022.
    DOI: 10.1190/image2022-3746066.1, Preprint: arXiv:2208.01209 [math.NA]
  2. Nonlinear seismic imaging via reduced order model backprojection.
    A.V. Mamonov, V. Druskin, and M. Zaslavsky, SEG Technical Program Expanded Abstracts: 2015, pp. 4375-4379.
    DOI: 10.1190/segam2015-5830429.1, Preprint: arXiv:1504.00094 [math.NA]
  3. Multiscale mimetic reduced-order models for spectrally accurate wavefield simulations.
    M. Zaslavsky, V. Druskin, and A.V. Mamonov, SEG Technical Program Expanded Abstracts: 2015, pp. 3710-3715.
    DOI: 10.1190/segam2015-5872011.1, Preprint: arXiv:1406.6923 [math.NA]
  4. S-fraction Multiscale Finite-volume Method for Spectrally Accurate Wavefield Simulations.
    A.V. Mamonov, V. Druskin and M. Zaslavsky, 77th EAGE Conference and Exhibition 2015.
    DOI: 10.3997/2214-4609.201413311
  5. Optimal Grid Coarsening: A Fast Proxy for Large Reservoir Optimization.
    A.V. Mamonov, B. Couet, W.J. Bailey, M. Prange, H.A. Djikpesse and V. Druskin,
    SPE/EAGE Reservoir Characterization and Simulation Conference, Abu Dhabi, UAE, October 2007.
    DOI: 10.2118/111378-MS

Preprints

  1. Slice sampling tensor completion for model order reduction of parametric dynamical systems.
    A.V. Mamonov, M.A. Olshanskii, submitted, 2024.
    Preprint: arXiv:2411.07151 [math.NA]
  2. Reduced order modeling for hyperbolic systems with application to multiparameter acoustic waveform inversion.
    L. Borcea, J. Garnier, A.V. Mamonov, J. Zimmerling, submitted, 2024.
  3. A priori analysis of a tensor ROM for parameter dependent parabolic problems.
    A.V. Mamonov, M.A. Olshanskii, submitted, 2023.
    Preprint: arXiv:2311.07883 [math.NA]

Book Chapter

Thesis

Reports

  1. Data-to-Born transform for inversion and imaging with waves.
    A.V. Mamonov joint with L. Borcea, V. Druskin and M. Zaslavsky.
  2. Back-projected reduced-order models for solving inverse acoustic scattering problems.
    M. Zaslavsky joint with V. Druskin and A. Mamonov.
    Oberwolfach Reports 14(2):1463-1549, 2017.
    DOI: 10.4171/OWR/2017/24, PDF: OWR_2017_24.pdf
  3. Model reduction method for a parabolic inverse resistivity problem.
    A.V. Mamonov joint with L. Borcea, V. Druskin and M. Zaslavsky.
  4. Efficient Reconstruction Algorithms for Inverse Problems in Quantitative Photoacoustic Imaging.
    K. Ren joint with H. Gao, A.V. Mamonov and H. Zhao.
  5. Solution of large scale PDE inverse problems in model reduction framework.
    V. Druskin joint with L. Borcea, A.V. Mamonov, V. Simoncini and M. Zaslavsky.
    Oberwolfach Reports 9(4):3061-3127, 2012.
    DOI: 10.4171/OWR/2012/51, PDF: OWR_2012_51.pdf

Presentations