# Solving the Brachistochrone Problem by an Influence Diagram

## TL;DR

This paper demonstrates how influence diagrams, a decision-theoretic graphical model, can be applied to solve the classical Brachistochrone problem, providing a novel approach and numerical validation.

## Contribution

It introduces a new method using influence diagrams to solve the Brachistochrone problem, contrasting with traditional calculus-based solutions.

## Key findings

- Influence diagrams can effectively model the Brachistochrone problem.
- Numerical experiments show the influence diagram solution closely matches the optimal solution.
- The paper provides R code for reproducibility.

## Abstract

Influence diagrams are a decision-theoretic extension of probabilistic graphical models. In this paper we show how they can be used to solve the Brachistochrone problem. We present results of numerical experiments on this problem, compare the solution provided by the influence diagram with the optimal solution. The R code used for the experiments is presented in the Appendix.