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UID:20261120-applied-math-seminar@jiazhaomath.github.io
DTSTAMP:20261007T000000Z
DTSTART:20261120T170000Z
DTEND:20261120T175000Z
SUMMARY:Applied Mathematics Seminar: Kirill Golubnichiy — A Semi-Discrete
  Convexification Method Combined with Deep Learning for Electrical Impedan
 ce Tomography
DESCRIPTION:Kirill Golubnichiy\, Postdoc\, Department of Mathematics & Stat
 istics\, Texas Tech University\nA Semi-Discrete Convexification Method Com
 bined with Deep Learning for Electrical Impedance Tomography\nIn this talk
 \, we develop a new semi-discrete version of the Carleman estimate-based c
 onvexification method\, a globally convergent numerical approach for nonli
 near inverse problems. The semi-discrete convexification method is used to
  generate an accurate starting point for the subsequent deep learning trai
 ning procedure. An important feature of the continuous convexification met
 hod is that its convergence to the true solution does not require the avai
 lability of a sufficiently accurate initial guess.\n\nWe introduce a new c
 oncept of (h)-strong convexity\, where (h) denotes the grid step size in t
 he semi-discrete formulation. This property enables us to derive an a prio
 ri accuracy estimate for the starting point supplied to the deep learning 
 stage. The proposed approach is applied to the highly nonlinear inverse pr
 oblem of Electrical Impedance Tomography. Numerical experiments involving 
 complicated conductivity structures demonstrate the accuracy\, robustness\
 , and computational feasibility of the combined semi-discrete convexificat
 ion and deep learning procedure.\nhttps://jiazhaomath.github.io/seminar/20
 26-2027.html#2026-11-20
URL:https://jiazhaomath.github.io/seminar/2026-2027.html#2026-11-20
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