A PDE-informed optimization algorithm for river flow predictions
Numerical Algorithms - Trang 1-16 - 2023
Tóm tắt
An optimization-based tool for flow predictions in natural rivers is introduced assuming that some physical characteristics of a river within a spatial-time domain
$$[x_{\min }, x_{\max }] \times [t_{\min }, t_{\textrm{today}}]$$
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
$$[t_{\min },t_{\textrm{today}}]$$
. Using these data, given
$$t_{\textrm{future}} > t_{\textrm{today}}$$
and a forecast of the flow-rate at
$$x=x_{\min }$$
and
$$t=t_{\textrm{future}}$$
, 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
$$x \in [x_{\min }, x_{\max }]$$
and
$$t=t_{\textrm{future}}$$
. 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.
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