A machine learning algorithm for water control
Résumé
Most flow and contaminant transport models (at least the most realistic ones) are based on conservation laws translated into partial differential equations. Analytical solutions to these problems can rarely be calculated, especially when combined with a control strategy. Numerical simulation tools are therefore implemented. Whatever the method used, with or without a mesh, points are chosen in the spatial and temporal domains where the solution will be approximated. These points can be seen as nodes of a (large) graph whose edges, for the examples discussed here, represent physical characteristics and system control. The method we propose consists in interpreting an optimal control problem as a graph optimization problem, its topological structure and the weighting of its edges. In particular, we have developed an algorithm based on the optimal permutation of the edges of the graph, which allows to converge, via gradient descent, to the minimum of any sufficiently regular loss function.