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Faculty of Mathematics

 

I am an Assistant Research Professor at DAMTP, and a member of the Cambridge Hub for Innovative Mathematics in Research and Applications CHiMIRA.

I completed my PhD at the University of Klagenfurt, and have since held postdoctoral positions at the University of Graz and the Max Planck Institute for Solar System Research.

My research lies at the intersection of regularization theory, nonlinear dynamical inverse problems, and data-driven methods. I was awarded the GIP Prize on Inverse Problems for the best PhD thesis in inverse problems across German-speaking countries (2020–2022).

Broadly, I explore:

  • Regularization and novel reconstruction: all-at-one, bi-level, one-shot strategies
  • Partial differential equations: nonlinear, time-dependent, well-posedness
  • Inverse problems in PDEs: parameter estimation, model discovery
  • Machine learning: data-driven physics, discretization by neural networks
  • Data assimilation: real-time estimation, model reference adaptation
  • Passive imaging: random media, correlation-based techniques

My work is inspired by a range of applications:

  • Medical imaging: magnetic particle imaging, Landau-Lifshitz-Gilbert eq.
  • Cell biophysics: traction force microscopy, hyperelasticity, active force densities, Stokes equations
  • Helioseismology: solar differential rotation, viscous-inertial wave modeling
  • Reaction-advection-diffusion: hidden nonlinear laws, Fisher eq., Lane-Emden eq., Zeldovic-Frank-Kamenetskii eq.
  • Aeroacoustic: source detection, optimal experimental design
  • Heat phenomena: inverse heat source, optimal sensor placement

Come take a peek at my personal homepage to see what I’ve been working on!

Publications

Sequential bi-level regularized inversion with application to hidden reaction law discovery
TTN Nguyen
(2024)
Bi-level iterative regularization for inverse problems in nonlinear PDEs
TTN Nguyen
– Inverse Problems
(2024)
40,
045020
Inferring solar differential rotation and viscosity via passive imaging with inertial waves
TTN Nguyen, T Hohage, D Fournier, L Gizon
(2024)
Bi-level iterative regularization for inverse problems in nonlinear PDEs
TTN Nguyen
(2023)
Learning-Informed Parameter Identification in Nonlinear Time-Dependent PDEs
C Aarset, M Holler, TTN Nguyen
– Applied Mathematics & Optimization
(2023)
88,
76
Discretization of parameter identification in PDEs using neural networks
B Kaltenbacher, TTN Nguyen
– Inverse Problems
(2022)
38,
124007
Parameter identification for elliptic boundary value problems: An abstract framework and applications
H Hoffmann, A Wald, TTN Nguyen
– Inverse Problems
(2022)
38,
075005
Learning-informed parameter identification in nonlinear time-dependent PDEs
C Aarset, M Holler, TTN Nguyen
(2022)
On numerical aspects of parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
TTN Nguyen, A Wald
– Inverse Problems and Imaging
(2022)
16,
89
Discretization of parameter identification in PDEs using Neural Networks
B Kaltenbacher, TTN Nguyen
(2021)
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Research Group

Cambridge Image Analysis

Room

FL.03