ENGF0003 Mathematical Modelling and Analysis I Coursework Integrated Engineering Programme (IEP)

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Coursework Summary – Task 1 & Task 2

Task 1 – Describing and Visualising Data (30 marks)

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You will analyse and visualise open datasets about AI training compute.

A. Data Summary (15 marks)

• Use the dataset provided (Dataset 1).
• In MATLAB, create a table summarising the training compute requirements (petaFLOPS) for three AI domains of your choice (e.g. language, vision, robotics).
• Include descriptive statistics (mean, median, variance, etc.) that help interpret the data.
• If useful, apply a data transformation (e.g. log scale) to make results clearer, and justify mathematically why you did so.
• Write a short analysis paragraph explaining what your statistics mean and how the transformation helps interpretation.

B. Data Visualisation (15 marks)

• Create a graph/visualisation (e.g. bar chart, boxplot, line plot) in MATLAB showing differences in compute cost across the domains.
• Write a short analysis comparing the results in your table and figure.
• Explain how the visualisation supports, complements, or validates your summary table.

Goal: Show that you can describe, transform, and represent data effectively, and interpret it critically.

Task 2 – Modelling and Analysing Data (40 marks)

You will model the relationship between model size and power draw for AI training and analyse its implications.

A. Modelling Power Draw (20 marks)

• Use Dataset 2 for the Language domain.
• Fit a curve (mathematical model) showing power draw vs. number of parameters (e.g. exponential, polynomial, power-law).
• Present your results in a table like this:

• Explain why you chose this type of curve, what each column means, and evaluate the quality of your fit.
• Then find an estimate of ChatGPT-5’s number of parameters (from reliable online sources) and use your fitted model to estimate its training power draw.
• Discuss how trustworthy your sources and estimates are.

B. Impact Discussion (20 marks)

• Using your findings from Tasks 1 and 2, discuss the potential social, environmental, and economic impacts of AI compute and energy costs.
• Make a logical, evidence-based argument using your results and datasets, and relevant external research.
• You can include your own reflections and opinions if they’re supported by data.

Goal: Show you can build a quantitative model, justify it, use it to make estimates, and discuss real-world implications.

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