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 scientific machine learning and uncertainty quantification (L1)
Sensitivity analysis (L2)
Linear regression and Bayesian linear regression (L3)
Gaussian process regression (L4)
Neural networks and deep neural networks (L5)
Neural networks for scientific machine learning: PINNs, GNNs, Neural ODEs (L6)
Unsupervised learning: PCA, generative models (L7)
Uncertainty propagation and inverse problems: Monte Carlo sampling, Bayesian calibration (L8)
Approximate Bayesian inference: MCMC, variational inference (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.
• Apply deep neural networks to accelerate scientific computing and interpret the results.

Indicative reading list

Reading lists can be found in Talis

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