Introductory description

N/A.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Introduction to uncertainty, probability and statistics (L1-2)
Sensitivity analysis (L3)
Linear regression (L4)
Uncertainty propagation using Monte Carlo sampling (L6)
Surrogate models - Gaussian process regression (L5), Polynomial Chaos (L7)
Inverse problems (L8)
Guest lecture on advanced topics in predictive modelling (L9)

Learning outcomes

By the end of the module, students should be able to:

• Demonstrate knowledge of statistical and mathematical methods for predictive modelling.
• Perform detailed, advanced analyses of complex data sets, extracting information and developing relationships using linear and nonlinear regression and classification techniques.
• Systematically develop models for predictive purposes using advanced techniques of model selection and evaluation.
• Understand and apply cutting-edge methods of machine learning.
• Demonstrate an understanding of complex modelling transferability issues arising from, e.g. choices of exchange-correlation functionals and pseudo-potentials in electronic structure, or the choice of force fields in atomistic and molecular models.
• Demonstrate a detailed knowledge of, and be able to apply models, for quantifying uncertainties arising in material structure and properties, constitutive models, from limited data scenarios and through coarse graining.

Indicative reading list

The recommended textbook is:

McClarren, Uncertainty Quantification an Predictive Computational Science, available from SpringerLink on campus at Warwick - aimed at a general Physical Sciences / Engineering audience
For a more mathematical viewpoint, some students may be interested in:

Sullivan, Introduction to Uncertainty Quantification, available from SpringerLink on campus at Warwick
Familiarity with vectors, matrices and basic linear algebra at the level taught in most undergraduate physical sciences and engineering courses will be assumed. If you would like to refresh your knowledge on this topic you may find the following resources useful:

Boyd and Vandenberghe, Introduction to Applied Linear Algebra - Vectors, Matrices and Least Squares, freely available online. Companion exercises that implement the material in Python and Julia are available from the same webpage.
Where appropriate, specific lectures also point to additional textbooks for relevant topics.

Subject specific skills

Demonstrate knowledge of statistical and mathematical methods for predictive modelling
Perform detailed, advanced analyses of complex data sets, extracting information and developing relationships using linear and nonlinear regression and classification techniques
Systematically develop models for predictive purposes using advanced techniques of model selection and evaluation
Understand and apply cutting-edge methods of machine learning
Demonstrate an understanding of complex modelling transferability issues arising from, e.g. choices of exchange-correlation functionals and pseudo-potentials in electronic structure, or the choice of force fields in atomistic and molecular models.
Demonstrate a detailed knowledge of, and be able to apply models, for quantifying uncertainties arising in material structure and properties, constitutive models, from limited data scenarios and through coarse graining.

Transferable skills

Mathematical analysis, statistics, coding, writing