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Department of Computer Science and Technology



Course pages 2023–24

Machine Learning and the Physical World

Principal lecturer: Prof Neil Lawrence
Additional lecturer: Dr Carl Henrik Ek
Taken by: MPhil ACS, Part III
Code: L48
Term: Michaelmas
Hours: 16
Class limit: max. 30 students
Prerequisites: A good background in statistics, calculus and linear algebra. A machine learning module such as Machine Learning and Bayesian Inference ( or equivalent is highly recommended.
Moodle, timetable


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.

  1. 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.
  2. Real world decisions have consequences which may have costs, and often these cost functions need to be assimilated into our machine learning system.
  3. 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


Week 1: Introduction to the unit and foundation of probabilistic modelling

Week 2: Gaussian processes and probablistic inference

Week 3: Simulation and Sequential decision making under uncertainty

Week 4: Emulation and Experimental Design

Week 5: Sensitivity Analysis and Multifidelity Modelling

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=.


  • Two individual tasks (15% each)
  • Group Project (70%). 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.

Recommended Reading

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press

Bishop, C. (2006). Pattern recognition and machine learning. Springer.

Laplace, P. S. (1902). A Philosophical Essay on Probabilities. John Wiley & Sons.