IRTG Modern Inverse Problems (MIP)

Education

10/2018 – 06/2022: Ph.D. Candidate, IRTG at RWTH Aachen University, Germany

04/2018 – 09/2018: Doctoral Student at AICES Graduate School, RWTH Aachen University, Germany

04/2016 – 03/2018: Master of Science in Mathematics, RWTH Aachen University, Germany

10/2012 – 03/2016: Bachelor of Science in Mathematics, RWTH Aachen University, Germany

Research Interests

• bayesian inversion
• optimal experimental design
• variational data assimilation and optimal control
• uncertainty quantification
• model order reduction, in particular reduced basic methods
• multilevel methods
• parameter estimation

Data Assimilation and Sensor Selection for Configurable Forward Models: Challenges and Opportunities for Model Order Reduction Methods
Doctoral Thesis, IRTG-2379, RWTH Aachen, Germany, 2021

A Certified Reduced Basis Method for Parametrized 3D-VAR Data Assimilation, 
Master’s Thesis, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Germany 2018

A Space-Time Finite Element Method for Discretization of the Heat Equation,
Bachelor’s Thesis, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Germany, 2016

1. 3D-VAR for parameterized partial differential equations: a certified reduced basis approach
   Nicole Aretz-Nellesen, Martin A. Grepl, and Karen Veroy
   Advances in Computational Mathematics 45, 2369-2400 (2019)
   doi: 10.1007/s10444-019-09713-w
2. A sequential sensor selection strategy for hyper-parameterized linear Bayesian inverse problems
   Nicole Aretz-Nellesen, Peng Chen, Martin A. Grepl and Karen Veroy
   In Numerical Mathematics and Advanced Applications ENUMATH 2019 (pp. 489-497). Springer, Cham.
3. Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study
   Alex Viguerie, Alessandro Veneziani, Guillermo Lorenzo, Davide Baroli, Nicole Aretz-Nellesen, Alessia Patton, Thomas E. Yankeelov, Alessandro Reali, Thomas J. R. Hughes & Ferdinando Auricchio
   Comput Mech (2020), 66 (5), pp. 1131–1152
   doi: 10.1007/s00466-020-01888-0
4. Sensor selection for hyper-parameterized linear Bayesian inverse problems
   Nicole Aretz, Peng Chen, Karen Veroy
   PAMM 20.S1 (2021)
   doi: 10.1002/pamm.202000357