The use of data-driven methods in engineering and scientific applications has been growing considerably in the past decades with the advent of modern techniques, dedicated hardware, and data availability. Extracting information from data to improve decision-making in many different fields is one of the main pillars of the modern scientific machine learning framework. The current state-of-the-art of engineering applications - which comprises the use of expensive simulations originating from numerical methods to approximate complex and nonlinear transient partial differential equations (PDEs) - can also benefit by learning from data. Subjects such as dynamical systems model discovery, model order reduction, physics-informed neural networks, and control have been widely explored in recent years with data-driven approaches and applied to diverse applications such as fluid dynamics, neuroscience, turbulence, epidemiology, and finance. However, since data fuel these approaches, one must be cautious regarding I/O operations. Nowadays, the disparity between computing and I/O speed makes it very difficult for large simulations to output to disk a large amount of data to be analyzed later. This disparity is particularly true when seeking accurate solutions for the numerical discretization of PDEs, where the state vectors obtained from the nonlinear systems are likely high-dimensional (i.e., the use of fine meshes on finite element simulations) and require substantial storage space when saved into disk. Consequently, data should be analyzed while the simulation is running, and/or data reduction computations should be performed to reduce the amount of data saved to disk. Another issue that arises from time-demanding simulations or time-critical problems is that the complete data is available only after the end of the simulations. The use of on-the-fly algorithms for data-driven methods able to update the model with the addition of new snapshots will be explored in this talk. In this case, with real-time snapshot generation, one can analyze and steer numerical parameters during runtime and perform real-time diagnostics on time-variant systems and real-time predictions. In this talk, we present these enhancements to the Dynamic Mode Decomposition (DMD) workflow, a data-driven method based on snapshots. We will introduce data compression in the DMD workflow and discuss how in situ visualization strategies can be embedded. We consider different data compression strategies applied to snapshots and evaluate the accuracy of the results. We assess the storage efficiency of lossless and lossy compression methods with different accuracy thresholds. Then, we evaluate the use of DMD on the resulting data to assess how the compression affects the reconstruction/prediction accuracy. Since such simulations demand a significant amount of time to complete, we also apply streaming DMD on the data generated using in situ visualization tools (more precisely, Paraview Catalyst) at runtime. In this case, images generated by Paraview Catalyst scripts are input for streaming DMD, where each snapshot is assessed and used to update the modes if it contains relevant information. The relative errors in the results, the error between approximated and original pixel values from the images, are also compared using different metrics. We also address a critical question: what if the snapshots do not have the same dimension? In other words, how can we cope with snapshots coming from adaptive mesh refinement and coarsening simulations? Finally, theoretically and numerically, we also demonstrate that when performing DMD on a fully coupled PDE system with a compartmental structure, one may recover predictive behavior.
Bio: ALVARO L. G. A. COUTINHO got a master's and DSc (1987) in Civil Engineering from The Alberto Luiz Coimbra Institute for Graduate Studies and Research in Engineering (COPPE), The Federal University of Rio de Janeiro, Brazil, where he is a professor since 1998. He served in various positions at COPPE. He is currently Coordinator of the Interdisciplinary Area of Computational Engineering and Science at COPPE.
DDPS webinar: https://www.librom.net/ddps.html
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