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            <title xml:lang="en">A machine learning algorithm for water control</title>
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            <funder>As part of the La Rochelle Territoire Zéro Carbone (LRTZC) initiative, the authors also received support from funding provided by the Plan d’Investissement d'Avenir (PIA) through the Territoires d’Innovation de Grande Envergure (TIGA), managed by the Caisse des Dépôts, as well as from the Région Nouvelle-Aquitaine. The work also received France 2030 funding under the reference ‘ANR-23-EXMA-0007'</funder>
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                <title xml:lang="en">A machine learning algorithm for water control</title>
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              <p>Most flow and contaminant transport models (at least the most realistic ones) are based onconservation laws translated into partial differential equations. Analytical solutions to theseproblems can rarely be calculated, especially when combined with a control strategy.Numerical simulation tools are therefore implemented. Whatever the method used, with orwithout a mesh, points are chosen in the spatial and temporal domains where the solution willbe approximated. These points can be seen as nodes of a (large) graph whose edges, for theexamples discussed here, represent physical characteristics and system control.The method we propose consists in interpreting an optimal control problem as a graphoptimization problem, its topological structure and the weighting of its edges. In particular, wehave developed an algorithm based on the optimal permutation of the edges of the graph, whichallows to converge, via gradient descent, to the minimum of any sufficiently regular lossfunction.</p>
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