Revision as of 14:41, 1 July 2024

Abstract

This article provides a summary of our latest research, where we investigate the application of data-driven deep learning methods to simulate the dynamics of physical systems that are governed by partial differential equations (PDEs). The main challenge is the long-term temporal extrapolation for fluid dynamics problems that exhibit steep gradients and discontinuities. We make use of deep learning techniques, specifically designed for time-series predictions like LSTM, TCN, and Attention mechanism, as well as CNN. These methods are employed to model the dynamics of systems primarily influenced by advection. We propose a combination of a Convolutional Autoencoder (CAE) model for data compression and a novel CNN-based for forecasts. These models take a series of high-fidelity vector solutions and predict the solutions for the following time steps using auto-regression. To reduce complexity and computational demands during both online and offline stages, we implement deep auto-encoder networks. These techniques are used to compress the high-fidelity snapshots before feeding them into the forecasting models. Our models are evaluated on numerical benchmarks, such as the 1D Burgers’ equation and Stoker’s dam-break problem, to assess their long-term predictive accuracy, even in scenarios that extrapolate beyond the training domain. The model that demonstrates the highest accuracy is subsequently used to simulate a hypothetical dam break in a river with real 2D bathymetry. Due to space constraints, only a selection of results is showcased, with additional findings available in our work [1] and the newer ones will also be presented in the talk. Our findings indicate that the proposed CNN future-step predictor offers significantly accurate forecasts in the considered spatiotemporal problems.

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