A PDE-informed optimization algorithm for river flow predictions

n optimization-based tool for flow predictions in natural rivers is introduced assuming that some physical characteristics of a river within a spatial-time domain [x_min, x_max] × [t_min, t_today] are known. In particular, it is assumed that the bed elevation and width of the river are known at a finite number of stations in [x_min, x_max] and that the flow-rate at x=x_min is known for a finite number of time instants in [t_min,t_today] . Using these data, given t_future > t_today and a forecast of the flow-rate at x=x_min and t=t_future , a regression-based algorithm informed by partial differential equations produces predictions for all state variables (water elevation, depth, transversal wetted area, and flow-rate) for all x ∈ [x_min, x_max] and t=t_future . The algorithm proceeds by solving a constrained optimization problem that takes into account the available data and the fulfillment of Saint-Venant equations for one-dimensional channels. The effectiveness of this approach is corroborated with flow predictions of a natural river.