The module “Machine Learning and the Physical World” is focused on machine learning systems that interact directly with the real world. Building artificial systems that interact with the physical world have significantly different challenges compared to the purely digital domain. In the real world data is scares, often uncertain and decisions can have costly and irreversible consequences. However, we also have the benefit of centuries of scientific knowledge that we can draw from. This module will provide the methodological background to machine learning applied in this scenario. We will study how we can build models with a principled treatment of uncertainty, allowing us to leverage prior knowledge and provide decisions that can be interrogated.

There are three principle points about machine learning in the real world that will concern us.

We often have a mechanistic understanding of the real world which we should be able to bootstrap to make decisions. For example, equations from physics or an understanding of economics. Real world decisions have consequences which may have costs, and often these cost functions need to be assimilated into our machine learning system. The real world is surprising, it does things that you do not expect and accounting for these challenges requires us to build more robust and or interpretable systems. Decision making in the real world hasn’t begun only with the advent of machine learning technologies. There are other domains which take these areas seriously, physics, environmental scientists, econometricians, statisticians, operational researchers. This course identifies how machine learning can contribute and become a tool within these fields. It will equip you with an understanding of methodologies based on uncertainty and decision making functions for delivering on these challenges.


You will gain detailed knowledge of

surrogate models and uncertainty surrogate-based optimization sensitivity analysis experimental design You will gain knowledge of

counterfactual analysis surrogate-based quadrature Schedule

  • Week 1: Introduction to the unit and foundation of probabilistic modelling
  • Week 2: Gaussian processes, inference and introduction to decision making
  • Week 3: Sequential decision making under uncertainty and Sensitivity Analysis
  • Week 4: Counter Factual Analysis and Experimental Design
  • Week 5: Machine Learning for Inverse problems
  • Week 6-8: Case studies of applications and Projects

Practical work

During the first five weeks of the unit we will provide a weekly worksheet that will focus on implementation and practical exploration of the material covered in the lectures. The worksheets will allow you to build up a these methods without relying on extensive external libraries. You are free to use any programming language of choice however we highly recommended the use of =Python=.


This unit will be assessed using a group project. Each group will work on an application of uncertainty that covers the material of the first 5 weeks of lectures in the unit. Each group will submit a report which will form the basis of the assessment. In addition to the report each group will also attend a short oral examination based on the material covered both in the report and the taught material.

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press http://www.gaussianprocess.org/gpml/

Bishop, C. (2006). Pattern recognition and machine learning. Springer. https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf

Laplace, P. S. (1902). A Philosophical Essay on Probabilities. John Wiley & Sons. https://archive.org/details/philosophicaless00lapliala

Further Information

Due to COVID-19, the method of teaching for this module will be adjusted to cater for physical distancing and students who are working remotely. We will confirm precisely how the module will be taught closer to the start of term.