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Hybrid AI based reduction of the shallow water system for flood plain simulations

Résumé

Reduced Order Models (ROMs) have been widely used to efficiently solve large-scale problems in many fields including computational fluid dynamics (CFD) [4]. ROMs techniques allow to replace the expansive Full Order Model (FOM), by a ROM that captures the essential features of the system while significantly reducing the computational cost. In this work, we elaborate on and evaluate a new reduced basis method referred to as EA-POD-NN [2] for model reduction of the shallow water equations, which combines Proper Orthogonal Decompo- sition (POD) with Artificial Neural Networks (ANNs). The method begins with the POD technique to construct reduced bases from high-resolution solutions and then utilizes deep ANNs to learn as- sociated coefficients in the reduced bases as it has been initially done in [3]. The method follows an offline-online strategy : the POD reduced basis, along with the training of the ANNs, are performed in an offline stage, enabling the surrogate model to be used for real-time predictions. The process is non-intrusive, as it does not require opening the high-resolution model code. Here, the proposed method additionally takes into account the POD-based projection error, enabling the attainment of higher accuracy while preserving a limited number of POD modes, even in the delicate situation of non-linear advection-dominated flows. The approach allows for the limitation of the output dimension of the ANNs, thus enabling the use of smaller ANNs with fewer parameters, the- refore a better interpretability and potentially smaller datasets. We further compare its performance with the original method, POD-NN derived in [3]. The developed method is evaluated on a real-world test case aimed at simulating inundation of the Aude river in Southern France, and relies on the open-source computational code DassFlow [1]. Results demonstrate that the proposed EA-POD-NN method provides satisfying accuracy for hydraulic variables such as water elevation and discharge. Overall, the method is promising for performing real- time simulations of floodplain dynamics in particular (but not only), offering a cost-effective approach for ROM of shallow water equations. [1] Dassflow (data assimilation for free surface flows). open source computational software. Project- team MathHydroNum (IMT/INSA Toulouse - INRAe Aix-en-Provence - ICUBE Strasbourg). https ://github.com/DassHydro. [2] M. Allabou, R. Bouclier, P. A. Garambois, J. Monnier. Reduction of the shallow water system by an error aware pod-neural network method : Application to floodplain dynamics. submitted (revised version). [3] J. S. Hesthaven, S. Ubbiali. Non-intrusive reduced order modeling of nonlinear problems using neural networks. Journal of Computational Physics, 363, 55–78, 2018. [4] A. Quarteroni, A. Manzoni, F. Negri. Reduced basis methods for partial differential equations : an introduction, vol. 92. Springer, 2015.
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Dates et versions

hal-04618157 , version 1 (20-06-2024)

Identifiants

  • HAL Id : hal-04618157 , version 1

Citer

Mustapha Allabou, Robin Bouclier, Pierre-André Garambois, Jerome Monnier. Hybrid AI based reduction of the shallow water system for flood plain simulations. CANUM 2024 - 46ème Congrès National d'Analyse Numérique, May 2024, Ile de Ré, France. ⟨hal-04618157⟩
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