N Tepetidis, Flood routing using artificial neural network models, Diploma thesis, 103 pages, Department of Water Resources and Environmental Engineering – National Technical University of Athens, Athens, November 2020.
We study the application of artificial neural networks for addressing civil engineering problems and more specifically flood routing which constitutes finding a mathematical representation of the spatio-temporal evolution of flood phenomena. In general, the flows observed in nature are unsteady and flood flows are no exception and thus generating a crucial scientific endeavor. Firstly, we study the performance of a multilayer neural network in estimating routing for the river Pinios. Parallelly, we introduce a new methodology for solving complex problems which are described by nonlinear partial differential equations. Namely, the methodology concerns the utilization of artificial neural networks that obey any given law of physics (known as Physics Informed Neural Networks or PINN). Based on the nature of the problem and the available data, we determine two classes of problems: those that aim at finding the solution of the equation that describes the physical problem and those that aim at estimating the parameters of the equation for a given known solution. As in most of the civil engineering problems, flood routing is accurately described by the partial differential equations, known as Saint-Venant equations, which do not have an analytical solution. The robustness of our method is examined by solving the Burgers equation, for which an analytical solution is available. From the three wave models that are derived by the Saint-Venant equations, we analyze the model of the kinematic wave through an application, while we also compare with a solution obtained through a numerical finite differences method. We observe that PINNs can both estimate the solution of this differential equation and inversely estimate its parameters given the solution, with high accuracy.
Full text (2703 KB)