# Goal quest for an intelligent surfer moving in a chaotic flow

arXiv: https://arxiv.org/abs/2307.00019 · HTML: https://mlsanity.com/paper/2307.00019/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 37 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 1 of 1)

- [Google matrix analysis of directed networks](https://mlsanity.com/paper/1409.0428/) (2014)

## Abstract (arXiv)

We consider a model of an intelligent surfer moving on the Ulam network generated by a chaotic dynamics in the Chirikov standard map. This directed network is obtained by the Ulam method with a division of the phase space in cells of fixed size forming the nodes of a Markov chain. The goal quest for this surfer is to determine the network path from an initial node A to a final node B with minimal resistance given by the sum of inverse transition probabilities. We develop an algorithm for the intelligent surfer that allows to perform the quest in a small number of transitions which grows only logarithmically with the network size. The optimal path search is done on a fractal intersection set formed by nodes with small Erd"os numbers of the forward and inverted networks. The intelligent surfer exponentially outperforms a naive surfer who tries to minimize its phase space distance to the target B. We argue that such an algorithm provides new hints for motion control in chaotic flows.