Computational Science: Uncertainty Quantification & Data-driven Modelling

The course provides essential techniques for handling uncertainty and data in computational models. You will learn to quantify uncertainty, estimate unknown parameters, and construct fast surrogate models to accelerate simulations. You will also explore how observational data can be integrated into computational frameworks to improve accuracy and reliability.

Topics covered

• Key concepts in uncertainty quantification (UQ): verification vs. validation, intrusive vs. non-intrusive methods, forward vs. inverse UQ
• Numerical methods for PDEs with random parameters: stochastic Galerkin and collocation
• Bayesian inference for parameter estimation
• Sampling techniques: Monte Carlo and importance sampling
• Gaussian processes for surrogate modeling
• Model reduction: projection-based and data-driven approaches
• Data assimilation using Kalman filters

The course is relevant for anyone interested in advanced computational methods and can be included as an elective in the Master’s programme in Mathematics and Numerical Analysis, Computational Science, and Applied Computational Science. It can also be taken as a standalone course.

Teaching combines lectures with assignments designed to support learning and prepare you for the final oral exam. While assignments are not mandatory, they provide valuable practice in applying advanced numerical methods to real computational problems. You will also complete a project where theory meets application, culminating in a written project report and an oral examination. The oral exam determines whether you receive a “Pass” or “Pass with Distinction.” 

The course prepares you for advanced studies and research in computational science, applied mathematics, and engineering. The skills you acquire are highly relevant in fields where modelling, simulation, and data analysis are central, including climate science, biomedical engineering, finance, and industrial design. You will be well equipped for roles in scientific computing, data-driven modelling, simulation based decision making, and research and development in both academia and industry.

Entry requirements

Admission to the course requires English 6/b and at least 90 credits in natural sciences or engineering, of which at least 45 credits should be in mathematics and/or numerical analysis, including knowledge corresponding to the courses NUMA01 Computational Programming with Python, 7.5 credits, MASA02 Mathematical Statistic, Basic Course, 15 credits, and NUMN32 Numerical Methods for Differential Equations, 7.5 credits.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.