Optimizing Function Selection for Modeling Complex Systems

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SUMMARY

The discussion focuses on the challenge of selecting appropriate mathematical functions for modeling complex systems, specifically in programming contexts. The user seeks a tool that allows them to sketch functions and receive recommendations on suitable mathematical forms, such as exponential or polynomial functions. A practical example provided involves determining the optimal running speed in the rain to minimize water exposure, highlighting the need for a function E(v) that correlates velocity with the area exposed to rain. The conversation emphasizes the importance of defining boundary conditions and utilizing binary logic for modeling physical states.

PREREQUISITES
  • Understanding of mathematical functions (exponential, polynomial, etc.)
  • Familiarity with programming concepts and function modeling
  • Basic knowledge of statistical analysis and boundary conditions
  • Experience with empirical data collection and graphing
NEXT STEPS
  • Research tools for function approximation, such as MATLAB or Python libraries like SciPy
  • Learn about curve fitting techniques and their applications in modeling
  • Explore statistical methods for defining boundary conditions in physical models
  • Investigate mathematical modeling of real-world scenarios, focusing on physics-based problems
USEFUL FOR

Computer programmers, data scientists, mathematicians, and anyone involved in modeling complex systems or optimizing mathematical functions for practical applications.

Mephisto
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I do a lot of computer programming and often times i have a very clear idea of a function i need to model something, but i have no idea what kind of function would be good to model it, or how to vary its parameters to get what i need etc.

what i need is some way to sketch the function using just mouse or something, and a program that would tell me what kind of function would best approximate what I had in mind. for example, exponential, polynomial, tan inverse, some combination of those? Does anyone know of a program/procedure that does something like this?

Math forum is the best place i could find for this, I'm sorry if its not an exact fit.
 
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Use binary logic [0 and 1] to model the physical states you are studying. You can then arbitrarily define boundary conditions for 0 and 1 and examine them statistically.
 
hi, I'm sorry but i don't really understand what you mean. What are the physical states? For example, last time i was trying to determine what speed you have to run in the rain to minimize the amount of water you come to contact with (get least wet). I needed to have a function E(v), where given velocity v, I would get back the Extra area exposed to the vertical rain (since you are lifting your legs so that rain can strike those too). I could graph the function E(v) from just empirical observations, roughly, but i couldn't translate the thing into math! I didn't know what function to use in my calculations.
And I have no idea how I would apply your solution to something like this. what would be the physical states?
 

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