Permanent Faculty
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Allan Peter Engsig-Karup, Associate professor
Keywords: numerical analysis, differential equations, high-performance computing, machine learning, uncertainty quantification, finite element methods, numerical algorithms, scientific computing, mathematical modelling, iterative methods for large system of equations, model reduction
I do teaching and research in applied computational mathematics and engineering science. My research focus on modelling and advanced simulation relevant for development of useful proofs-of-concepts (theoretical/practical) for exploiting new modern technologies and improving scientific algorithms and applications. I work at interfaces of math modelling, applied mathematics, statistics and programming to enable scientific computations on modern powerful computers of scientific and engineering relevance. read more
Dimitri Boiroux, Associate ProfessorKeywords: diabetes technology, mathematical modelling, scientific computing, model-based control, model predictive control, state estimation, parameter estimation, Kalman filter, differential equations
I am broadly interested in mathematical modeling and scientific computing. In particular, I have conducted research about model identification and validation, numerical optimization, linear and nonlinear model predictive control, adaptive control and scientific computing of ordinary differential equations. My main field of application so far was biological systems, e.g. for the control of blood glucose in people with diabetes and patients in the intensive care unit. read more
John Bagterp Jørgensen, ProfessorKeywords: systems and control, numerical optimization, numerical solution of differential equations, model predictive control, process control and optimization, scientific computing
My research is focused on model predictive control for industrial energy and chemical systems, medical systems, and systems within economics and finance. This involves developing new computational methods for model predictive control. Much of the research is in collaboration with industrial companies. read more
Kim Knudsen, Associate professorKeywords: Applied mathematical analysis, Inverse Problems, Partial Differential Equations, Functional Analysis, Medical Imaging, Tomography, Biomathematics, Mathematical Biology, Uncertainty Quantification, Scientific Computing
Kim Knudsen has a background in applied mathematical analysis, which concerns the mathematical modelling, analysis and numerical computations for real world physical phenomena. During the last 20 years he has contributed significantly to the reconstruction problem in Electrical Impedance Tomography by advancing the theory in the partial data problem and by developing and investigating so-called direct reconstruction methods in 2D and 3D. In recent years his interest has been devoted to the theoretical and computational understanding of Hybrid Data Tomography, e.g. Acousto-Electric Tomography and Magnetic Resonance Electrical Impedance Tomography. Besides his works on Inverse Problems, Kim Knudsen has worked on mathematical biology within aquatic sciences. read more
Michael Pedersen, Professor, Head of sectionKeywords: modern analysis, PDEs, boundary value problems for linear and non-linear PDEs, regularization methods, variational analysis, control theory for PDEs, boundary control, pseudodifferential analysis, mathematical biology
By use of pseudodifferential boundary calculus I study the control of boundary value problems, and lately by the use of the Hilbert Uniqueness Method I have worked with functional analytic formulation of boundary control problems, invoking elements from the so called Boutet de Monvel-calculus and studying exponential stability. In mathematical biology we have studied spatio-temporal predator--prey models in several dimensions and other nonlinear problems, as well as delay PDEs for species spreading. These are also connected to pollution propagation in mathematical ecology. read more
Mirza Karamehmedovic, Associate ProfessorKeywords: analysis, differential equations, partial differential equations, pseudodifferential boundary problems, inverse problems, inverse scattering, inverse source problems, Uncertainty Quantification
I use the theory of partial differential equations and of pseudodifferential operators to characterize general inverse scattering and inverse source problems in terms of solution regularity, as well as stability in the presence of noise. A 'byproduct' of the analysis are, for example, new results concerning the mapping properties of special classes of pseudodifferential operators. On the numerical side, I construct and apply numerical methods for the approximate solution of industrially relevant inverse scattering problems. Here, I have lately begun to include elements of PDE-based Uncertainty Quantification and rudimentary machine learning. Spectral and regularity analysis of solutions of boundary problems. Numerical solution of inverse problems for PDE. Uncertainty Quantification. read more
Martin Skovgaard Andersen, Associate ProfessorKeywords: optimization, numerical linear algebra, scientific computing
My research focuses on convex optimization and its applications in science and engineering. I am particularly interested in large-scale conic and semidefinite optimization and algorithms that exploit some kind of mathematical structure (such as sparsity or rank stucture) in order to solve large, challenging optimization problems faster. read more
Per Christian Hansen, ProfessorKeywords: uncertainty quantification, inverse problems, matrix computation, regularization methods
Per Christian Hansen is a VILLUM Investogator and his research focuses on computational methods for the solution of large mathematical and engineering problems. His main research area concerns the numerical solution of inverse problems in, e.g., tomography and iamge deblurring. His work on numerical methods for regularization is internationally recognized. His h-index is 48 (March 2019) and he is a SIAM Fellow. Per Christian Hansen is professor of Scientific Computing at the Department of Informatics and Mathematical Modelling. He was awarded the Danish Dr. Techn. doctoral degree in 1996 from DTU in the area of numerical analysis. He has spent several research visits at American universities, such as Stanford University, UCLA, Emory University, and Tufts University. Per Christian Hansen teaches numerical algorithms and inverse problems. He has published 4 books on numerical methods and inverse problems and more than 100 scientific papers in international journals. read more
Peter Røgen, Associate ProfessorKeywords: Differential geometry, topology of curves, topology of surfaces, protein structures, protein structure classification, protein structure prediction
My research is based on a mixture of differential geometry and low dimentional topology reffeared to as geometric knot theory. Starting from basic mathematical research and general industrial applications, my main focus turned to adaption of the consept of knot invariants to geometric invariants for the open string structures of proteins and RNA. Geometric invariants provides fast methods for structural description, comparison, clustering, and automatic classification of protein structures and are amongst the very few methods that mathematically can detect the type of “topological” changes biologists use to define protein fold classes. My metric interest in proteins configuration space carries on in what I call metric training of knowledge-based potentials for protein structure prediction. It may be seen as reverse engineering the best possible potential energy function where best is specified by a metric. read more
Yiqiu Dong, Associate ProfessorKeywords: numerical linear algebra, matrix computation, inverse problems, variational methods, regularization methods, mathematical image processing, tomography reconstruction, optimization
My main research topic is imaging related inverse problems. The main tool that I use is variational methods, i.e., combining Bayesian statistics and regularisation techniques to propose suitable minimisation problems that mathematically describe the inverse problems and its desired solutions. Then, I apply as well as develop advanced optimisation algorithms for solving the proposed minimisation problems. Recently I have also begun to introduce uncertainty quantification technique into inverse problems. read more
PhDs, Postdocs and Faculty
Coming soon.