{"id":10352,"date":"2023-10-09T06:00:14","date_gmt":"2023-10-09T10:00:14","guid":{"rendered":"https:\/\/blogs.mathworks.com\/student-lounge\/?p=10352"},"modified":"2023-10-08T19:32:50","modified_gmt":"2023-10-08T23:32:50","slug":"differential-equations-modeling-with-matlab-scudem","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/student-lounge\/2023\/10\/09\/differential-equations-modeling-with-matlab-scudem\/","title":{"rendered":"Differential Equations Modeling with MATLAB – SCUDEM"},"content":{"rendered":"
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Joining us today is Wesley Hamilton, who is a STEM Outreach Engineer here at MathWorks. Wesley will talk about SIMIODE’s SCUDEM competition. Wesley, over to you\u2026 <\/span><\/div>\n

Overview<\/h2>\n
This blog post has three goals:<\/div>\n
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  1. Introduce SIMIODE’s SCUDEM competition, which MathWorks now supports,<\/li>\n
  2. Show how one might start developing a model to address a real world (SCUDEM) problem, and<\/li>\n
  3. Showcase the ODE solving functionality provided by MATLAB.<\/li>\n<\/ol>\n
    We’ll be showcasing how a new team to SCUDEM, and math modeling, might<\/span> get started developing a solution to a problem. As such the model won’t be particularly refined, but the modeling process employed can (and should) be replicated as a better practice when competing.<\/div>\n
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    Table of Contents<\/span><\/div>\n

    Overview
    \n<\/a>    SIMIODE and SCUDEM
    \n<\/a>    The problem
    \n<\/a>    An initial model – plan
    \n<\/a>    An initial model – implementation in MATLAB
    \n<\/a>    Next steps
    \n<\/a>    Functions<\/a><\/p>\n<\/div>\n<\/div>\n

    SIMIODE and SCUDEM<\/h2>\n
    The Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE) is an organization that, as described on their website<\/a>, “is a Community of Practice focused on a modeling first method of teaching differential equations”. Since 2017, SIMIODE has organized the SIMIODE Challenge Using Differential Equations Modeling (SCUDEM). This annual competition has teams pick one of three problems, and develop a differential equation model to answer their chosen problem. This year SCUDEM will run from October 20 to November 30, in which time teams will develop their models and prepare a short youtube video describing their work. The SCUDEM website<\/a> has more information on taking part, including registration information and problems and results from previous years.<\/div>\n
    This year, MathWorks is excited to provide direct support for SCUDEM by way of licenses and preparatory materials. Read on for some of these new preparatory materials.<\/div>\n

    The problem<\/h2>\n
    For this blog post, we’re going to tackle the 2022 SCUDEM problem A, which ask teams to develop a model that describes ISS astronauts’ stress when completing tasks and helping\/getting helped by ISS visitors. Take a minute to read through the problem statement in its entirety by going to https:\/\/qubeshub.org\/community\/groups\/scudem\/wiki\/SCUDEMVII2022,<\/a> and then click on “Problem Statements” underneath “Official Challenge Problems for SCUDEM VII 2022”. A PDF with all three of the 2022 problem statements will be downloaded.<\/div>\n
    Before setting up a model, we need to have a solid grasp of the actual problem we’re being asked to address. Here, let’s walk through the problem statement paragraph by paragraph and pick out key pieces that will help us specify what exactly we’re building a model for.<\/div>\n
    A group of individuals recently purchased a flight to go to the International Space Station [1]. Each of them had to complete a rigorous training regime and demonstrate that they were capable of handling the physical and mental demands of space travel. When they arrived, they were expected to provide help and assistance to the astronauts who were at the station and the new crew members had a large number of tasks and experiments to complete. <\/span><\/div>\n
    In the model we develop, we’re going to specify two different groups of people that may behave (and be modeled) differently. Since the ISS has a smaller number of crew, we have two options to explore:<\/div>\n
      \n
    1. follow a more agent-based model approach, where we keep track of individual astronauts and visitors, or<\/li>\n
    2. treat the astronauts and visitors as single entities, so that we’re modeling e.g. the collective stress of the astronauts and not individuals’ stress.<\/li>\n<\/ol>\n
      Either approach can work, and both approaches may not be difficult to implement in MATLAB. Let’s read on to see what other information might inform which of these options we’ll pick.<\/div>\n
      The hectic schedule nearly overwhelmed the newly arrived guests, and the extra attention they required added to the stress felt by the existing crew. What can be done to ease this burden, yet result in a more efficient use of time for a flight crew? Before answering this question, a way to model the stress and capabilities of a flight crew must be created. <\/span><\/div>\n
      A key piece of information is that “stress” and “capabilities” are explicitly mentioned. At this point, these may be the two quantities we build a model around for each group or each astronaut\/visitor. Moreover, the specific mention that the visitors added to the stress of the astronauts is important – when we test our model, we may want to run a simulation without visitors to confirm that the stress of the astronauts is stable (in some capacity), since the provided information suggests that the visitors potentially threw things out of stability.<\/div>\n
      Develop a mathematical model of the stress and capabilities of a group of people. Assume that there is an existing group of people in place at the destination who are already under a great deal of pressure to complete their assigned tasks. The model should include the addition of a second group of capable people who arrive after undergoing the stress of a space launch and do not have prior exposure to the new environment. Given the expected stress levels over time what is the impact on the whole group? <\/span><\/div>\n
      This paragraph has the main task: Develop a mathematical model of the stress and capabilities of a group of people<\/span>. As above, we’re still looking at focusing on stress and capability as the two numeric quantities to use, and the specific mention of a group<\/span> of people suggests it’s not out-of-line to treat all astronauts as a single entity (the group<\/span> of astronatus), and same with the visitors. Otherwise, we’re being asked to say something about stress levels over time – if in the end we don’t want to keep track of both stress and capabilities, then we should definitely keep stress as the main quantitative object we work with.<\/div>\n
      Your model should be able to take a schedule for the whole group and then predict the impact on the group of people. You should identify what happens under different scenarios including the expectation of an immediate high level of productivity, a short period of rest followed by a sharp rise in a high level of productivity, and then a gradual increase from low to high levels of productivity. Which scenario results in the lowest stress and highest net productivity? Also, what should ground observers expect from small deviations from a given schedule? <\/span><\/div>\n
      Here we’re given a few more specific requirements to include:<\/div>\n
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      1. incorporate a schedule for the astronauts and visitors,<\/li>\n
      2. incorporate different levels of productivity for all onboard,<\/li>\n
      3. incorporate (small) deviations in the schedule.<\/li>\n<\/ol>\n
        All of this should be incorporated to say something about the long-term stress of everyone onboard.<\/div>\n
        So to summarize (some of) what we’ve picked out of the problem statement:<\/div>\n