In large language models, a “prompt” refers to the input text provided to the model to instruct or guide it to produce specific outputs. Its main function is to inform the model about what kind of information the user wants to obtain or what kind of task they want to complete.
For example, when using a large language model for text generation, you can input a question, a description, or a topic as a prompt, and the model generates relevant answers or content based on this input. The quality and clarity of the prompt greatly influence the relevance and accuracy of the model’s output. In simple terms, a prompt is like an instruction or request given to the model, telling it what the user hopes it will do.
So, what are some good prompts for mathematical modeling competitions?
Here is a better prompt for your reference:
Assume you are an expert in mathematical modeling, and I am a college student participating in a mathematical modeling competition. I need your help to solve the problems in the competition. Please think and assist me according to the following guidelines:
(1) Understanding the Problem Background:
Read and restate the key points of the problem. How did this problem arise, and which fields are related?
Are there similar cases or problems? How were they solved? What can we learn from relevant papers?
(2) Proposing Assumptions and Variables:
Based on the actual situation, what assumptions can be made to simplify the problem? How might these assumptions affect the results?
Identify the key variables in the problem and their interrelationships. Are these relationships linear, nonlinear, or something else?
(3) Classifying the Problem:
What type of problem does this belong to, such as evaluation, prediction, optimization, or graph theory? What is the type of each sub-question?
(4) Constructing the Mathematical Model:
What mathematical equations or inequalities will be used to describe the relationships between these variables? Is there a need to introduce auxiliary variables or parameters?
Considering the nature of the problem, which model should be chosen? What reference papers are there for similar problems?
(5) Solutions and Optimization:
Based on the established model, what should the preliminary solution be? What different methods are available?
What criteria or indicators will be used to evaluate the effectiveness of the solutions, such as accuracy, efficiency, reliability, or practicality?
If there are shortcomings, how can the model be optimized? Can performance be improved by adjusting parameters, improving algorithms, or introducing new data?
(6) Practical Applications and Limitations:
In practical applications, what challenges might this model encounter? How can we respond to these challenges?
Identify and discuss the limitations of the model. What improvements can we make regarding these limitations?
Please provide detailed and feasible problem-solving ideas and steps in your answers. Additionally, during the analysis, multiple problem-solving approaches can be given for the same problem, and it should be evaluated which solution is easier to implement.
If data is needed, please indicate how to obtain it.
(All subsequent answers should be in Chinese)
Here is my mathematical modeling competition problem:
(Please replace this topic with your own)
2023 ICM
Problem E: Light Pollution
Background
Light pollution is used to describe any excessive or poor use of artificial light. Some of the phenomena that we refer to as light pollution include light trespass, over-illumination, and light clutter. These phenomena are most easily observed as a glow in the sky after the sun has set in large cities; however, they may also occur in more remote regions.
Light pollution alters our view of the night sky, has environmental impacts, and affects our health and safety. For example, plant maturation may be delayed or accelerated, and migration patterns of wildlife affected. Excessive artificial light may confuse our circadian rhythms, leading to poor sleep quality and perhaps physical and mental health issues. Glare caused by artificial lights may contribute to some motor vehicle accidents.
Community officials or local groups may implement intervention strategies to mitigate the negative effects of light pollution. Artificial light, however, has both positive and negative effects that impact different locations in different ways. For example, to avoid the negative impacts of light pollution listed above, some communities opt for low-light neighborhoods, which in turn might lead to increased crime. The impacts of light pollution may depend on factors such as the location’s level of development, population, biodiversity, geography, and climate.
Therefore, assessing the extent of the effects and the potential impacts of any intervention strategies must be tailored to a specific location.
Requirement
COMAP’s Illumination Control Mission (ICM) is working to promote awareness of the impacts of light pollution and develop intervention strategies to mitigate those impacts. In support of this ICM work, your task is to address measuring and mitigating the effects of light pollution in various locations, incorporating both human and non-human concerns. Specifically, you should:
Develop a broadly applicable metric to identify the light pollution risk level of a location.
Apply your metric and interpret its results on the following four diverse types of locations:
a protected land location,
a rural community,
a suburban community, and
an urban community.
Describe three possible intervention strategies to address light pollution. Discuss specific actions to implement each strategy and the potential impacts of these actions on the effects of light pollution in general.
Choose two of your locations and use your metric to determine which of your intervention strategies is most effective for each of them. Discuss how the chosen intervention strategy impacts the risk level for the location.
Finally, for one of your identified locations and its most-effective intervention strategy, produce a 1-page flyer to promote the strategy for that location.
Glossary
Artificial Light: Any non-naturally occurring source of light.
Circadian Rhythms: The natural 24-hour sleep-wake cycle on which humans and other organisms operate.
Glare: Excessive brightness that decreases one’s ability to see.
Intervention Strategies: Policies and/or actions that could be taken to disrupt the negative impacts of light pollution.
Light Clutter: Excessive grouping of lights.
Light Trespass: When light enters unintended areas.
Over-Illumination: Lighting at an intensity higher than what is needed for an activity or location.
Protected Land: Areas that governments or private entities protect from development due to their ecological, cultural, and/or natural importance.
Rural Community: A community located in one of the least densely populated parts of a country or region, and not easily accessible from an urban community.
Suburban Community: A community located in a moderately densely populated part of a country or region, or easily accessible from an urban community.
Urban Community: A community located in one of the most densely populated parts of a country or region.
For example, I am interested in the metrics in this model, and we can continue to ask:
Let’s look at the response from chatgpt:
Of course, you may also find this model too simple, and we can ask chatgpt to modify the model:
Let’s look at the modified model:
If you don’t know how to introduce this model, you can ask like this:
Let’s look at chatgpt’s response:
From the examples above, it is clear that using large language models can greatly assist the modeling process. Students with capability are recommended to use chatgpt4.
Students who do not like to tinker can also use the domestic Wenxin Yiyuan, and it is recommended to use version 4.0 of Wenxin Yiyuan, which is priced at one-third of chatgpt4, and its capability is between chatgpt3.5 and chatgpt4.