Downscaling shallow water simulations using artificial neural networks and boosted trees

Killian Bakong (1) , Vincent Guinot (1, 2) , Antoine Rousseau (1, 3) , Gwladys Toulemonde (1, 3)

1 LEMON - Littoral, Environment: MOdels and Numerics
2 HSM - Hydrosciences Montpellier
3 IMAG - Institut Montpelliérain Alexander Grothendieck

We present the application of two statistical artificial intelligence tools for multi-scale shallow water simulations. Artificial neural networks (ANNs) and boosted trees (BTs) are used to model the relationship between low-resolution (LR) and high-resolution (HR) information derived from simulations provided in the learning phase. The two statistical models are analyzed (and compared) through hyper-parameters such as the number of epochs and the network structure for ANNs, and the learning rate, tree depth and number for BTs. This analysis is performed through 4 numerical experiments the input datasets of which (for the learning, validation and test phases) are varied through the boundary conditions of the flow numerical simulation. The performance of the ANNs is remarkably consistent, regardless of the choice made for the training/validation/testing set. The performance improves with the number of epochs and the number of neurons. For a given number of neurons, a single-layer structure performs better than multi-layer structures. BTs perform significantly better than ANNs in 2 experiments, with an error 10 to 100 times lower and a computational cost 5 to 10 times larger). However, when the validation datasets differ from the training datasets, the performance of BTs performance is strongly degraded, with a modelling error more than one order of magnitude larger than that of ANNs. Used in conjunction with upscaled flood models such as porosity models, these techniques appear as a promising operational alternative to direct flood hazard assessment from HR flow simulations.

Mots clés: Shallow water equations; multi-scale simulation; artificial neuron networks; boosted trees

Domaines: Modélisation et simulation; Intelligence artificielle [cs.AI]; Statistiques [math.ST]; Mécanique des fluides [physics.class-ph]; Risques

Killian Bakong, Vincent Guinot, Antoine Rousseau, Gwladys Toulemonde. Downscaling shallow water simulations using artificial neural networks and boosted trees. Discrete and Continuous Dynamical Systems - Series S, 2023, 16 (2), pp.220-239. ⟨10.3934/dcdss.2022198⟩. ⟨hal-03818928v2⟩