Evolution style algorithm to determine EOM

[ian_dsouza]

I had seen a documentary about an algorithm that uses notions of evolution to deduce the equation of motion of a system by sampling a variable connected with the system.

For example, they used the double pendulum case where they sampled the position of the free end of the pendulum and arrived at the equation of motion using curve fitting. For example, if there was a Π/2 in the equation, it would show up as 1.5707.

Here's my vague recollection of how they did it. They used a lot of candidate functions like, x, x^2, exp(x), exp(2x), etc. As you process the samples, some functions better fit the data than others and hence "survive" while the others "die" out. Eventually as the number of samples tends to infinity, the resultant equation tends to the true equation of motion of the system.

The algorithm is very likely in an open source package.

If anyone's heard of something like this, could you please tell me how I could find more info on it.

 

[AndyW]

Thank you for sharing your interest in this algorithm. I am familiar with the concept of using evolutionary principles to deduce equations of motion in systems. This approach, known as evolutionary computation, has been used in various fields of science and engineering to solve complex problems that cannot be easily solved using traditional methods.

The algorithm you are referring to is likely a form of evolutionary computation, specifically a genetic algorithm. In this method, a population of potential solutions (represented as equations in your case) are randomly generated and evaluated using a fitness function, which in your example is the fit of the equation to the data. The equations with the highest fitness are then selected to "reproduce" and create new equations, mimicking the process of natural selection.

Over time, as the algorithm iterates and more data is processed, the equations with the best fit to the data will "survive" and be refined, eventually converging towards the true equation of motion. This approach has been successfully applied in various fields, including physics, engineering, and computer science.

As for finding more information on this specific algorithm, I suggest searching for keywords such as "genetic algorithm", "equation of motion", and "double pendulum" in scientific databases or online search engines. You may also find helpful resources in open source packages or repositories related to evolutionary computation.

I hope this helps in your search for more information on this algorithm. Best of luck in your research endeavors.