2024年HIMCM美國中學數學建模競賽B題

中文賽題：高性能計算的環境影響分析

隨著全球對高性能計算（HPC）的需求在人工智能（AI）、數據科學和加密貨幣挖礦等領域持續增長，這些技術帶來的環境影響也隨之增加。依賴於(yu) 龐大的數據中心、高性能硬件和高耗能計算過程，引發了人們(men) 對其環境後果的關(guan) 注。

高性能計算的環境影響中，最關(guan) 鍵的方麵是能耗及其相關(guan) 的碳排放。這方麵尤為(wei) 重要，因為(wei) 能耗直接關(guan) 係到溫室氣體(ti) 排放，特別是當電力來源於(yu) 化石燃料時。HPC 設施通常消耗大量能源，導致其碳足跡顯著。此外，在可再生能源基礎設施有限的地區，能源需求可能給本地電網帶來壓力，增加對非可再生能源的依賴。

除了能耗，HPC的環境影響還包括多個(ge) 方麵：

• 水資源使用：許多數據中心使用水進行冷卻，導致大量水資源消耗，並可能因廢水排放而引發汙染。
• 電子垃圾：計算硬件的製造、使用和廢棄產生大量難以回收的電子垃圾。
• 資源消耗：生產HPC硬件涉及稀土材料的開采，可能破壞棲息地、汙染環境，並增加對能源的需求。
• 土地使用：數據中心所需的物理空間可能引發土地使用爭議，對當地生態係統產生影響。
• 空氣質量：化石燃料發電廠的排放會降低空氣質量並影響人類健康。此外，數據中心產生的細微顆粒物和粉塵也會影響本地空氣質量。
• 化學品使用：冷卻係統使用的化學品如果管理不當，可能產生泄漏或溢出，構成風險。
• 社會經濟影響：大型數據中心及資源開采可能引發土地變化，並對當地社區的能源可得性產生不公平影響。
• 噪音汙染：在此過程中每個階段使用的機械設備都會產生噪音汙染，影響社區和野生動物。
• 網絡架構：數據傳輸所需的網絡基礎設施要求更廣泛的連接，超出個體節點的需求。

其中許多方麵都有專(zhuan) 門的環境影響研究，您可以將其作為(wei) 了解問題的背景資料。

任務

1. 理解問題：描述 HPC 能力在全球範圍內的年能耗規模，考慮其在滿負荷和平均利用率下的情況。
2. 建立模型：建立一個全麵的模型，確定因能耗導致的 HPC 總碳排放的環境影響。考慮能源的生產方式，計算能源構成對碳排放的影響。
3. 應用模型：
   • 探討在 HPC 增長、其他領域能耗需求增加以及不同能源構成的可能情況下，模型如何隨時間變化。
   • 使用模型為2030年問題的規模提供現實的邊界值以獲得洞察。
4. 擴展模型並分析：
   • 模擬增加可再生能源比例對碳排放的減排效果，研究切換到 100% 可再生能源的影響及可能遇到的挑戰。
   • 細化模型（或開發新模型）以包含其他關鍵領域之一的環境影響，以更深入地了解HPC的影響。描述選擇該領域的原因及其與其他關鍵領域的關係，尤其是能耗。
5. 分享模型及其結果：
   • 提出一套可操作的建議，以減少 HPC 的環境影響，包括技術和政策導向的解決方案。
   • 假設其中一項建議被采納，展示如何將其納入模型。
   • 聯合國谘詢委員會於2024年9月發布了一份關於人工智能的報告，題為 “為人類管理人工智能”，其中沒有大量涉及高性能計算。^[1]給谘詢委員會寫一封一到兩頁的信，敦促他們在 2030 年的預定發展目標中加入有關高性能計算對環境影響的更詳細章節。用您的研究結果和建議來支持這一請求。

你的PDF解決(jue) 方案不超過 25 頁，包括：

• 一頁總結
• 目錄
• 完整解決方案
• 一至兩頁的聯合國谘詢委員會信函
• 參考文獻
• AI使用報告（如使用，不計入 25 頁限製）

注意：沒有特定的最低頁數要求。可使用最多 25 頁完成所有解決(jue) 方案工作及附加信息（如圖表、圖解、計算、表格）。接受部分解決(jue) 方案。允許謹慎使用生成式 AI 工具（如ChatGPT），但非必要。如使用生成式 AI，需遵循 COMAP 的 AI 使用政策，並將 AI 使用報告附加在 PDF 的最後部分，不計入 25 頁限製。

HiMCM/MidMCM最新：在線提交流程

本文旨在幫助和指導參與(yu) HiMCM/MidMCM 的學生和指導老師。COMAP 在文中提供了關(guan) 於(yu) 新的在線提交流程的信息，需使用新的在線提交頁麵（提交鏈接）。完成提交時，你需要準備好團隊控製編號、指導老師ID和所選問題編號。

術語表

• 高性能計算：即高效能計算（HPC），指使用超級計算機和並行處理技術以高速度解決複雜計算問題。
• 電子垃圾：指丟棄的電器或電子設備，包括廢棄的計算機、智能手機、電視等。由於含有有害物質，電子垃圾是一個顯著的環境問題。
• 數據中心：用於容納計算係統及相關組件的設施，包括服務器、冷卻係統及備用電源，以確保可靠運行。
• 節點：網絡基礎設施中任何可發送、接收或處理數據的設備，即數據傳輸的節點。
• 滿負荷：電廠或能源來源在最優條件下的最大輸出，通常以兆瓦（MW）或吉瓦（GW）為單位，代表峰值發電能力。
• 平均利用率：衡量電廠或能源來源在特定時間段內的實際輸出與滿負荷的比值，表明設施相較於其最大潛力的運行情況。
• 能源構成：滿足能源需求的不同能源來源的組合，包括化石燃料（煤、石油、天然氣）、可再生能源（太陽能、風能、水電、生物質能）和核能。
• 化石燃料：從古代有機物中提取的能源，主要包括煤、石油和天然氣。燃燒化石燃料會產生溫室氣體排放。
• 可再生能源：來自自然不斷補充的來源的能源，如太陽能、風能、水電、地熱和生物質能。此類能源通常更具可持續性，環境影響較低。
• 核能：通過核裂變釋放的能量，盡管碳排放量較低，但涉及放射性廢物及核安全問題。

Problem: Examining the Environmental Impact of High-Powered Computing

As global demand for high-powered computing (HPC) continues to rise in sectors like artificial intelligence (AI), data science and cryptocurrency mining, so does the environmental footprint of these technologies. The increasing reliance on massive data centers, high performance hardware, and energy-intensive computational processes has sparked concern about their environmental consequences.

The most important aspect of the environmental impact of HPC is energy consumption and its associated carbon emissions. This aspect stands out as it has a direct contribution to climate change as energy consumption directly correlates with greenhouse gas emissions, particularly when electricity is generated from fossil fuels. These HPC facilities often consume vast amounts of energy, making their carbon footprint significant. Additionally, the energy demand can strain local power grids, especially in areas with limited renewable energy infrastructure leading to a higher reliance on non-renewable energy sources.

In addition to energy consumption, there are other environmental concerns. The additional environmental impacts of HPC are multi-faceted and can be categorized into several key areas:

• Water Usage. Many data centers use water for cooling leading to substantial water consumption and potential pollution with the discharge of their wastewater.
• E-Waste. The manufacturing, use and disposal of computing hardware contributes to electronic waste with many of the components being difficult to recycle.
• Resource Depletion. The production of HPC hardware involves the extraction of rare earth materials which can lead to habitat destruction, pollution, and additional demands for energy.
• Land Use. The physical space required for the data centers can lead to land use debates with significant impacts on the local ecosystems.
• Air Quality. This focuses on the emissions from fossil fuel power plants that can degrade air quality and affect human health. Additional consideration should also be given to fine particulate matter and dust generated by the data centers that impacts local air quality.
• Chemical Use. The cooling systems use chemicals that can pose a risk if not managed properly, including potential spills or leaks.
• Socioeconomic Impacts. Large data centers as well as the mining for resources can lead to changes in the land with the potential for inequities in energy access for local communities.
• Noise Pollution. All the operations involving machinery in every phase of this process can contribute to increased noise pollution impacting communities and wildlife.
• Network Architecture. The network infrastructure needed for data transmission extends beyond individual nodes to include greater connectivity concerns.

Many of these aspects have dedicated research into their environmental impacts that you can research and use as background into understanding the problem.

Requirements.

1. Understand the Problem. Describe the scope of this problem in terms of the annual energy consumption of the HPC capabilities worldwide considering both full capacity and average utilization rates.
2. Create Your Model. Develop a comprehensive model to determine the environmental impact of total carbon emissions resulting from energy consumption of HPC. Consideration should be given to how the energy is produced, accounting for energy mixes.
3. Apply Your Model.
   • Explore how your model may change in the future with the growth of HPC, the increasing demand for energy in other sectors and the potential for different energy sources and mixes.
   • Use your model to provide realistic bounds that can provide insight into the scope of the problem in the year 2030.
4. Expand Your Model and Reflect on Your Analysis.
   • Model the impact of increasing the portion of renewable energy and calculate the corresponding reductions in carbon emissions. Investigate the effects of switching to a 100% renewable energy source as well as the potential challenges involved.
   • Refine your model (or develop a new model) to include the environmental impact of one of the other key areas listed above to further understand the impact on HPC. Describe why your group chose that aspect and how it relates to other key areas, especially energy consumption.
5. Share Your Model and its Results.
   • Develop a set of actionable recommendations to reduce the environmental impact of HPC, considering both technical and policy-oriented solutions.
   • Assume one of your recommendations is acted upon. Determine and show how you can incorporate this into your model.
   • The United Nations Advisory Board issued a report on AI entitled “Governing AI for Humanity” in September 2024 without significantly addressing HPC.^[1]Write a one-to-two-page letter to the Advisory Board urging them to include a more detailed section on the environmental impacts of HPC in their scheduled developmental goals for 2030. Use your findings and recommendations to support this plea.

Your PDF solution of no more than 25 total pages should include:

• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• One- to two-page IOC letter
• References list.
• AI Use Report (If used does not count toward the 25-page limit.)

Note: There is no specific required minimum page length for a complete HiMCM submission. You may use up to 25 total pages for all your solution work and any additional information you want to include (for example: drawings, diagrams, calculations, tables). Partial solutions are accepted. We permit the careful use of AI such as ChatGPT, although it is not necessary to create a solution to this problem. If you choose to utilize a generative AI, you must follow the COMAP AI use policy. This will result in an additional AI use report that you must add to the end of your PDF solution file and does not count toward the 25 total page limit for your solution.

NEW HiMCM/MidMCM: Online Submission Process The purpose of this article is to assist and guide students and advisors participating in HiMCM/MidMCM. In the article, COMAP, provides information about the new online submission process using the new online submission page https://forms.comap.org/242386224483964. You will need your team's control number, advisor id number and your problem choice to complete your submission.

Glossary

• High-Powered Computing: Also known as high-performance computing (HPC), this refers to the use of supercomputers and parallel processing techniques to solve complex computational problems at high speeds.
• E-Waste: Short for electronic waste, e-waste refers to discarded electrical or electronic devices. This includes computers, smartphoness, televisions, and appliances that are no longer in use. E-waste is a significant environmental concern due to the hazardous materials it often contains.
• Data Centers: Facilities used to house computer systems and associated components. Data centers provide the infrastructure for processing, storing, and managing large volumes of data and include servers, cooling systems, and backup power supplies to ensure reliable operation.
• Node: A node in the context of network infrastructure is any device connected to a network that can send, receive, or process data. It's like a junction point where data can be transmitted, received, or modified.
• Full Capacity: The maximum output that a power plant or energy source can produce under optimal conditions. It is often expressed in megawatts (MW) or gigawatts (GW) and represents the peak generation capability.
• Average Utilization Rate: A measure of how effectively a power plant or energy source is being used over a specified period. It is calculated by dividing the actual output by the full capacity over the same period. This indicates how consistently a facility is operating compared to its full potential.
• Energy Mix: The combination of different energy sources used to meet energy needs. This can include fossil fuels (coal, oil, natural gas), renewable sources (solar, wind, hydro, biomass), and nuclear energy.
• Fossil Fuels: Energy sources derived from ancient organic matter, primarily coal, oil, and natural gas. These fuels are non-renewable and contribute to greenhouse gas emissions when burned.
• Renewable Energy: Energy that comes from sources that naturally replenish themselves, such as solar, wind, hydroelectric, geothermal, and biomass. These sources are generally considered more sustainable and have a lower environmental impact.
• Nuclear Energy: Energy produced through nuclear fission, where atomic nuclei are split to release energy. It is a low-carbon source but involves concerns regarding radioactive waste and nuclear safety.

Reference

[1]

United Nations Advisory Board on AI (2024). Governing AI for Humanity:https://sdgs.un.org/goals

[2]

Ahmed, M., & Verma, A. A review on the decarbonizetion of high performance computing centers, Journal of CLeaner Production, 2023:https://www.sciencedirect.com/science/article/pii/S0959652623004567

[3]

Goldman Sachs. AI is poised to drive 160% increase in data center power demand, 2023:https://www.goldmansachs.com