Inverse problems and stochastic methods research group
TalTech priority area
Research classification (Frascati)
Head of the research group
Research group member
Doctoral students
Keyword
inverse problems
fractional diffusion and wave motion
direct and inverse scattering
nonparametric statistics
Overview
The main directions of research are: Inverse problems for equations containingfractional derivatives. Inverse problemsfor linear and nonlinear fractional differential equations are studied. The unknowns to be determined are coefficients,source terms and kernels of generalizedfractional time derivatives. Such problemsoccur in modelling of diffusion and mechanical processes in porous, fractal andbiological media. The research is focusedon both theoretical aspects and elaborationof numerical methods. Direct and inverse scattering in singularand nonlocal media. Electromagnetic andacoustic direct and inverse scatteringin media with singularities or non-localfeatures is studied. Mathematical theory of tripole and more general multipoleantennas is developed. This branch iscomplemented by a development of newsignal processing on state-of-the-art computational methods for large-scale inverseproblems. Inverse problems to reconstructin homogeneities of media with non-localproperties by means of measurements ofscattered acoustic waves at boundariesare investigated. Elaboration of nonparametric statisticalmethods. The theory of nonparametricstatistical methods is developed and thesemethods are applied in environmental andbuilding engineering.
Important results
Main results of 2021: We proved that an energy of a far-fieldpattern scatted from a corner has alwaysa positive lower bound. This implies theimpossibility of invisibility cloaking of anobject with corners. We proved that a solution of the fractionaldiffusion-wave equation can be uniquelyrestored by means of final data providedboundary conditions are given in an arbitrarily small neighborhood of the finalvalue.
Related department
Department of cybernetics
Teadusgrupiga seotud publikatsioonid
- Janno, J. Inverse problems with unknown boundary conditions and final overdetermination for time fractional diffusion-wave equations in cylindrical domains // Mathematics (2021) vol. 9, 20, art. 2541, 22 p.
https://doi.org/10.3390/math9202541 - Blåsten, E.L.K., Pohjola, V. Cones with convoluted geometry that always scatter or radiate // Inverse Problems (2022) Vol. 38, Issue 12, Art. 125001.
https://doi.org/10.1088/1361-6420/ac963c - Blasten, E.L.K., Liu, H. Scattering by curvatures, radiationless sources, transmission eigenfunctions, and inverse scattering problems // SIAM Journal on Mathematical Analysis (2021) Vol. 53, Issue 4, p. 3801-3837.
https://doi.org/10.1137/20M1384002 - Rassõlkin, A., Rjabtšikov, V., Vaimann, T., Kallaste, A., Kuts, V. Concept of the test Bench for electrical vehicle propulsion drive data acquisition // 2020 XI International Conference on Electrical Power Drive Systems (ICEPDS), Saint-Petersburg, Russia, October 4-7, 2020. Danvers : IEEE, 2020. p. 35-42 : ill.
https://doi.org/10.1109/ICEPDS47235.2020.9249078 - Blasten, E., Liu, H. On corners scattering stably and stable shape determination by a single far-field pattern // Indiana University Mathematics Journal (2021) vol. 70, 3, p. 907-947.
https://doi.org/10.1512/IUMJ.2021.70.8411 - Blasten, E., Liu, H., Xiao, J. On an electromagnetic problem in a corner and its applications // Analysis & PDE (2021) vol. 14, 7, p. 2207-2224.
https://doi.org/10.2140/apde.2021.14.2207 - Huntul, M.J., Hussein, M.S., Lesnic, D., Ivanchov, M.I., Kinash, N. Reconstruction of an orthotropic thermal conductivity from non-local heat flux measurements // International journal of Mmthematical modelling and numerical optimisation (2020) vol. 10, 1, p. 102-122.
https://doi.org/10.1504/IJMMNO.2020.104327 - Blasten, E., Päivärinta, L.J., Sadique, S. Unique determination of the shape of a scattering screen from a passive measurement // Mathematics (2020) vol. 8, 7, art. 1156, 15 p.
https://doi.org/10.3390/math8071156 - Janno, J. Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data // Fractional calculus and applied analysis (2020) Vol. 23, 6, p. 1678–1701.
https://doi.org/10.1515/fca-2020-0083 - Janno, J., Kasemets, K., Kinash, N. Inverse problem to identify a space-dependent diffusivity coefficient in a generalized subdiffusion equation from final data // Proceedings of the Estonian Academy of Sciences (2022) vol. 71, 1, p. 3-15.
https://doi.org/10.3176/proc.2022.1.01 - Hyvönen, N., Päivärinta, L., Tamminen, J.P. Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps // Inverse problems & imaging (2018) vol. 12, 2, p. 373-400 : ill.
https://doi.org/10.3934/ipi.2018017 - Kinash, N., Janno, J. Inverse problems for a perturbed time fractional diffusion equation with final overdetermination // Mathematical methods in the applied sciences (2018) vol. 41, 5, p. 1925-1943 : ill.
https://doi.org/10.1002/mma.4719 - Kinash, N., Janno, J. An inverse problem for a generalized fractional derivative with an application in reconstruction of time- and space-dependent sources in fractional diffusion and wave equations // Mathematics (2019) vol. 7, 12, art. 1138, p. 1-16.
https://doi.org/10.3390/math7121138 - Janno, J., Kinash, N. Reconstruction of an order of derivative and a source term in a fractional diffusion equation from final measurements // Inverse problems (2018) vol. 34, 2, art. 025007, 19 p. : ill.
https://doi.org/10.1088/1361-6420/aaa0f0 - Kinash, N., Janno, J. Inverse problems for a generalized subdiffusion equation with final overdetermination // Mathematical modelling and analysis (2019) vol. 24, 2, p. 236–262.
https://doi.org/10.3846/mma.2019.016