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Section for Scientific Computing

We tackle complex mathematical and computational challenges in science and engineering. Analysing and solving these problems requires the interplay of advanced mathematical models, data analysis, and computer simulations. Our research in scientific computing focuses on developing the mathematical models and methods that make this possible.

Our research involves the complete scientific computing workflow, including model development, mathematical analysis, development of efficient computational methods, and numerical simulations. We address the challenges via collaborations with industrial users, engineers, and scientists for model development, data analysis, verification, etc. This involves student projects that prepare students to apply state-of-the-art mathematics to real-world problems.

We also perform research that zooms in on specific mathematical aspects. For example, we develop methods for data analysis that characterize and quantify the influence of measurement errors. Moreover, we design high-performance computing methods for handling large amounts of data in applications such as computed tomography, industrial design, and data analysis.

Education

Our broad expertise is part of the foundation for the Applied Mathematics (BSc) and Mathematical Modelling and Computation (MSc) programmes.

Students explore everything from advanced mathematical models and numerical simulations to high-performance computing while developing a computational mindset and strong problem-solving skills.

Head of Section

Martin Skovgaard Andersen

Martin Skovgaard Andersen Phone: +45 45253036 mskan@dtu.dk

Research areas

Computational Uncertainty Quantification

In Uncertainty Quantification (UQ) we characterize the sensitivity of a solution to errors in the data and models. This is critical for engineering design and analysis, where risks must be reduced as much as possible. One approach to dealing with this is to use novel and efficient spectral (high order) algorithms. In the CUQI project we develop the mathematical and computational framework for applying UQ to inverse problems such as deconvolution, image deblurring, tomographic imaging, source reconstruction, and fault inspection. We created a computational platform CUQIpy, suited for non-experts, which can be used by many different industrial and academic end users.

Lead researchers

Allan Peter Engsig-Karup Associate professor

Per Christian Hansen Professor

Inverse Problems

Inverse problems arise in areas such as tomography where we reconstruct the interior structures of an object from X-ray measurements. In inverse problems it is not possible to observe a phenomenon directly, only the indirect effect of the phenomenon can be measured. To solve the inverse problem, we need a mathematical model that allows us to determine the effect if we know the phenomenon. Solutions to inverse problems are extremely sensitive to errors in the data, and there may not be a unique solution to the problem. It is therefore necessary to use prior information to compute stable unique solutions using regularization algorithms.

Lead researchers

Per Christian Hansen Professor

Kim Knudsen Professor

Yiqiu Dong Associate Professor

Mathematical Modelling and Analysis

These areas, together with numerical simulation, are at the heart of scientific computing. Starting from complex challenges rooted in real-world applications, we provide a combination of mathematical and computational insight essential for discovery and innovation in science and engineering. This frequently involves ordinary, partial, or stochastic differential equations, complemented by uncertainty quantification. Applications include inverse problems in imaging and tomography, photonics, nanometrology, insulin and energy systems control, computational structural biology, and computational marine hydrodynamics.

Lead researchers

Michael Pedersen Professor

Kim Knudsen Professor

Mirza Karamehmedovic Associate Professor

Peter Røgen Associate Professor

Optimization and Control

These areas are central to solving many challenging problems across science and engineering. We develop optimization models and methods for a wide range of tasks, ranging from parameter estimation and data fitting to design and control of systems where some notion of system performance must be optimized while satisfying design goals and operational requirements. Automatic control complements this by enabling dynamic systems to respond intelligently to changing conditions. Our research covers both theory, practical implementations, and applications in, e.g., smart energy systems, medical systems, and process control.

Lead researchers

John Bagterp Jørgensen Professor

Martin Skovgaard Andersen Head of Section, Associate Professor

Yiqiu Dong Associate Professor

Scientific Machine Learning

In this area we combine data-driven modelling with domain-specific knowledge. We develop new, improved methods for complex problems in computational science and engineering, thereby enabling accelerated discovery in fields like physics, biology, and climate science. Our research involves both mathematical-physical modelling, methodological development, and applications in areas such as fluid dynamics.

Lead researchers

Allan Peter Engsig-Karup Associate professor

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