Computational Science: Approximating reality in the computer


Simulation and data analysis can be used in various disciplines such as biology, physics, medicine, economics, chemistry and geology to explore different processes. Models of reality can be built from data or known mathematical relationships to conduct experiments and ask questions about properties of the problem.


Reality can be measured by collecting different types of data or represented by mathematical models. Different questions about the data or the models can be translated into algorithms suitable for computers. The amount of available data and the complexity of the models used are growing rapidly. The computational and storage capacity of both personal computers and supercomputers have also developed rapidly. Less well known is that the evolution of algorithm efficiency has been similar.

In computational science, we investigate all parts of the process from mathematical formulation to efficient computer implementation. We develop efficient versions of fundamental algorithms in numerical linear algebra and optimization. We develop tailored methods for specific application areas such as life sciences, fluid dynamics, geosciences, quantum physics and financial mathematics. We perform research on infrastructures to handle large data sets such as cloud technology and on federated machine learning for sensitive data. We construct efficient parallel and distributed algorithms for specific types of hardware. A requirement in all method development is that the algorithms must be reliable in various ways. We analyze algorithms to be able to quantify their uncertainty in relation to given data and model assumptions and we also perform research in cyber security to be able to detect and counter various types of attacks on systems and algorithms.

  • Computational Science and Engineering (CSE): We construct computational methods for specific contexts such as glaciology or biomechanics.
  • Numerical analysis (NA): We analyse and develop efficient numerical methods.
  • Optimization: PDE-constrained optimisation, data-driven black box optimisation (Bayesian and surrogate-based methods, evolutionary optimisation), gradient-based methods.
  • Machine learning and Bayesian statistics: deep learning, statistical sampling, design of experiments, likelihood-free parameter inference, time series analysis, expectation-maximisation.
  • Computational Biology: deep learning for genomics, parameter inference of stochastic biochemical reaction networks, model exploration, stochastic simulation methods.
  • Numerical Quantum Dynamics: We develop and apply novel tools and techniques for solving the molecular time-dependent Schrödinger equation.

  • 1TD342: Introduction to Scientific Computing (5 credits)
  • 1TD352: Scientific Computing for Data Analysis (5 credits)
  • 1TD354: Scientific Computing for Partial Differential Equations (5 credits)
  • 1TD050: Advanced Numerical Methods (10 credits)
  • 1TD056: Applied Finite Element Methods (5 credits)