Non-Intrusive Data-driven Surrogate Models for Predicting Turbidity Currents Deposition from 3D Simulations

Resumo

Non-intrusive data-driven methodologies, such as POD-DL, offer a powerful approach for constructing surrogate models to address complex parametric problems. POD-DL integrates deep neural networks and follows a multi-step dimensionality reduction process, beginning with a linear reduction via Proper Orthogonal Decomposition (POD) and followed by a nonlinear reduction using a deep autoencoder. A subsequent nonlinear regression, implemented with a forward neural network, accounts for temporal and parametric coefficients.The framework involves numerous hyperparameters, including the number of POD basis modes, network architecture specifications, and typical neural network parameters like learning rate and batch size, all of which influence both training time and model accuracy. In a previous work, we applied this scheme to study gravity currents under the 2D lock-exchange configuration [3] for multiple angles of the initial configuration [4]. The angle of the channel served as a parameter, i.e., different angles generated different dynamics that were learned by the surrogate model. The regression neural network could then predict the dynamics for unseen angles.  Now, we extend the methodology to more realistic scenarios, a 3D channel-basin configuration for gravity currents, adapted from [5], analyzing variations in inlet velocities and sediment concentrations. Synthetic data were generated through large-scale parallel finite element simulations, allowing POD-DL to predict deposition maps for unseen parameter values. [1] M. Cracco et al., “Deep learning-based reduced-order methods for fast transient dynamics”, Arxiv Preprint 2212.07737, 2022. [2] S. Fresca and A. Manzoni, “POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition”, Comput. Methods Appl. Mech. Engrg., 2022. [3] V. K. Birman, B. A. Battandier, E. Meiburg, and P. F. Linden, “Lock-exchange flows in sloping channels”, Journal of Fluid Mechanics, 577:53–77, 2007. [4] R. M. Velho, A. M. Cortes, G. F. Barros,  F. A. Rochinha, and A. L. G. A. Coutinho, Advances in Data-Driven Reduced Order Models Using Two-Stage Dimension Reduction for Coupled Viscous Flow and Transport. Finite Elements in Analysis and Design, vol. 248, 2025.[5] T. Spychala, J. T. Eggenhuisen, M. Tilston and F. Pohl,The influence of basin setting and turbidity current properties on the dimensions of submarine lobe elements, SEDIMENTOLOGY, 2020.