Computational Science: Modelling in Computational Science

<p>The course gives an overview of fundamental modelling techniques in computational science. The students get an introduction to mathematical modelling of problems in the sciences and to how these models can be treated using computational methods. In particular, differential equation based models, machine learning for databased models, and Monte-Carlo methods for statistical models, are discussed.</p><p>The course treats:<br /> • Differential equation based modelling: Numerical methods to solve ODEs and convergence order. Applications to for instance predicting the spread of diseases and cell programming will be used.<br /> • MCMC based modelling: Central Limit Theorem, Metropolis-Hasting algorithm and error propagation will be covered with examples from statistical thermodynamics.<br /> • Machine learning and big data: We will cover the use of large data sets for creating models by training machine learning algorithms and which conditions are needed to create such models. This will be carried out on climate science applications.<br /> • Sources of errors in computational models, such as modeling errors, discretisation errors and statistical errors.<br /> • Relevant aspects concerning the fields possibilities to contribute to sustainable social development.</p>