Reconstruction of observed mechanical motions with Artificial Intelligence tools
This work addresses the challenge of modeling mechanical systems from observed data, which is incremental as it applies existing AI tools to a specific domain.
The paper tackled the problem of reconstructing observed mechanical motions by determining underlying laws using neural networks and the Extreme Learning Machine approach, successfully demonstrating reconstruction for both integrable and chaotic motions in examples like the gravity pendulum and double pendulum.
The goal of this paper is to determine the laws of observed trajectories assuming that there is a mechanical system in the background and using these laws to continue the observed motion in a plausible way. The laws are represented by neural networks with a limited number of parameters. The training of the networks follows the Extreme Learning Machine idea. We determine laws for different levels of embedding, thus we can represent not only the equation of motion but also the symmetries of different kinds. In the recursive numerical evolution of the system, we require the fulfillment of all the observed laws, within the determined numerical precision. In this way, we can successfully reconstruct both integrable and chaotic motions, as we demonstrate in the example of the gravity pendulum and the double pendulum.