Introductory description

This module provides students with knowledge in the modern field of scientific machine learning, which is a fusion of scientific computing and machine learning.

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.

• Bayesian linear regression and enhancements to it such as automatic relevance determination
• Gaussian process regression and enhancements such as sparse GP regression and the Kennedy-O'Hagan approach to model discrepancy.
• Kernel based ML-techniques including SVM and applications of reproducing kernel Hilbert spaces
• Dimensionality reduction as a tool for data analysis (PCA, kPCA, active subspaces)
• Advanced state space models such as the ensemble Kalman filter
• Neural networks and deep neural networks
• Neural differential equations and physics informed neural networks
• Advanced approximate Bayesian inference: variational inference, expectation maximisation, etc.

Learning outcomes

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

• Understand and interpret the application of Bayesian inference to infer model parameters from data
• Apply Gaussian process regression to build surrogate models for computational codes and evaluate the results
• Apply deep neural networks to accelerate scientific computing and interpret the results
• Synthesise neural network and mechanistic models and apply them to perform scientific machine learning
• Evaluate advanced inference techniques such as variational inference work and critique when they can be applied
• Recognise, formulate, analyse and interpret machine learning solutions to scientific problems
• Critique the application of machine learning methods to cutting edge problems in scientific computing

Indicative reading list

Bishop, Pattern Recognition and Machine Learning
MacKay, Information Theory, Pattern Recognition and Learning Algorithms
Rasmussen and Willians, Gaussian Processes for Machine Learning
Gelman, Bayesian Data Analysis
Hastie, The Elements of Statistical Learning: Data Mining, Inference and Prediction

View reading list on Talis Aspire

Interdisciplinary

The MSc programme will recruit students with backgrounds across the physical and mathematical sciences, including engineering, and will provide an interdisciplinary perspective on predictive modelling.

Scientific machine learning is a fusion of scientific computing and machine learning, drawing from mathematics, statistics and the modelling of physical phenomena across a wide range of application domains.

Subject specific skills

• Machine learning
• Computational statistics
• Predictive modelling
• Fusion of advanced data analysis and mathematical modelling techniques

Transferable skills

• Data analysis and modelling
• Oral presentation skills
• Scientific computing