Group assignment 1.6: Icy Dicey Propagation

An ice layer grows during a cold spell. How reliable is a prediction of its thickness after five days? You will use the Stefan ice-growth model to compare the uncertainty predicted by Taylor approximations with uncertainty obtained by Monte Carlo simulation.

You can preview this assignment in the MUDE 2026 workbook. The version without solutions remains available. The workbook also provides a ZIP download of the assignment files.

Friday group session: during the first three hours, work through the ice-growth notebook together and prepare handwritten reference notes. At 11:30, close all laptops. Your group will receive a separate set of questions to answer by hand, without computers or other resources (including AI tools). You may consult the handwritten notes prepared during the first three hours. Hand in your group’s handwritten answers at 12:30.

Before the session, read the uncertainty propagation chapter, complete Wednesday’s workshop (Pipe Dreams) and the programming assignment.

You will practice second-order mean propagation, first-order variance propagation, sampling a non-linear model, interpreting CDFs and checking the influence of input correlation. The written questions assess your mathematical reasoning and interpretation of your results, not your ability to recall Python syntax.

Files: icey_dicey.ipynb (preparation and numerical analysis) and report.md (the one-hour written questions, distributed when laptops close). The report is deliberately not included in the initial student download; teachers will provide it at 11:30.

By Lotfi Massarweh and Sandra Verhagen, Delft University of Technology. CC BY 4.0, more info on the Credits page of Workbook.