In these sample papers from M3 Challenge 2025, students in the U.S. and the U.K. were tasked with using mathematical modeling to understand and minimize the risk of power outages associated with heat waves. Each paper has a cover sheet that indicates what judges liked about the paper and what could have been improved.
“In this project we aimed to create models that would successfully predict information that’s relevant to how climate change and heatwaves are going to impact residents’ lives in Birmingham, UK…First, we created a model to predict indoor temperatures in heatwaves using linear regression. Following this, we analysed energy demand to find the maximum energy demand that the Birmingham grid should be prepared to handle during the summer months and how this could change over the next 20 years. Finally, we created an index to find the vulnerability of different boroughs and created a plan for the council to
spread resources more equitably to minimise the impact of power outages and heatwaves.”
“In this paper, we developed a model to predict the indoor temperature of non-air-conditioned dwellings in Birmingham, England, during a heatwave…Our model incorporates factors such as outdoor temperature variations, building materials, and window efficiency to simulate realistic indoor temperature fluctuations…We tested the model against actual heatwave data from Birmingham in July 2022 and fine-tuned our parameters for greater accuracy. Our results highlight the need for better cooling strategies in buildings without air conditioning, given the rising frequency of heatwaves and underscores the role of building materials and design in mitigating heat accumulation, which can help reduce health risks associated with extreme temperatures.”
“As global warming establishes a greater impact on the climate with each passing year, heat waves are a frightening reminder of the limits of air conditioning. The increasing intensity and length of heat waves can overwhelm even the recent improvements in cooling efficiency and housing infrastructure. Heat waves can also mean putting heavy strain on the power grid and increasing the risk of power outages, which can cut off access to both AC and critical health and communication systems. This is especially prevalent in low-income urban areas, which may have heavier reliance on what heat waves often compromise.”
“We examined the effect of heatwaves on cities and residential areas. Our model predicted that maisonnettes would have the highest peak internal temperature, and that all housing types would have a thermal inertia causing a lag between the peak ambient temperature and the peak internal temperature.
We also modelled the increase in peak demand capacity for a forecast horizon of 20 years, particularly examining the seasonality around the summer months. We established that the maximum demand increases over the period of 20 years we predicted for.
Finally, we use predictions from our examination of internal temperature fluctuation in buildings (question 1) to build a risk model that calculates the heat index in various municipalities of Birmingham. This risk model will allow health officials to provide targeted support to communities.”
