Kathrin Hellmuth

Downloadable CV

• Kathrin Hellmuth, Christian Klingenberg, Qin Li
  Preserving positivity of Gauss-Newton Hessian through random sampling
  submitted (2024)
   
• Herbert Egger, Kathrin Hellmuth, Nora Philippi, Matthias Schlottbom
  A kinetic chemotaxis model and its diffusion limit in slab geometry
  submitted (2024)
   
• Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang
  Reconstructing the kinetic chemotaxis kernel using macroscopic data: Well-posedness and ill-posedness
  accepted to SIAM Journal on Applied Mathematics (2024)
   
• Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang
  Kinetic chemotaxis tumbling kernel determined from macroscopic quantities
  SIAM Journal on Mathematical Analysis, vol. 56, no. 1, pp. 568-587 (2024)
   
• Kathrin Hellmuth, Christian Klingenberg
  Computing Black Scholes with Uncertain Volatility—A Machine Learning Approach
  Mathematics, vol. 10, no. 3, 489, special issue "Numerical Analysis with Applications in Machine Learning" (2022)
   
• Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang
  Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting
  Computation, vol. 9, no. 11, 119, special issue "Inverse Problems with Partial Data” (2021)

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  Conference proceedings:

• Kathrin Hellmuth, Christian Klingenberg, Qin Li
  Multi-scale PDE inverse problem in bacterial movement
  Hyperbolic Problems: Theory, Numerics, Applications. Volume II. HYP 2022. SEMA SIMAI Springer Series, vol 35 (2024), pp.395-405.
   
• Kathrin Hellmuth
  Inverse problems for kinetic equations - an application to chemotaxis
  Oberwolfach Reports.  Rep. 18 (2021), no. 3, pp. 2316–2318
   
• Kathrin Hellmuth
  An inverse problem for chemotaxis
  Oberwolfach Reports.  Rep. 18 (2021), no. 2, pp. 1080–1083

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  Science communication:

• Kathrin Hellmuth, Christian Klingenberg
  Route planning for bacteria
  Snapshots of modern mathematics from Oberwolfach (2022), no.12

Various natural phenomena can be described using partial differential equations (PDEs). They often contain parameters that fit the general description of the phenomenon to a concrete situation. Reconstructing these parameters from experimental data is called the inverse problem and is necessary to fit the model and to enable prognosis.

I investigate such a parameter identification problem for a model of bacterial motion stimulated by a chemical signal (like a food source), which is called chemotaxis. It is often modelled by a kinetic chemotaxis equation in which a parameter encodes the bacterial reaction to the chemical signal. Supposing to be given velocity independent measurements of the bacteria density, photographies for instance, I study whether such data can contain enough information to recover the kinetic parameter. Furthermore, I study the relation between the reconstruction from the kinetic and a corresponding macroscopic Keller-Segel model.