Data-driven Model Reduction of Turbulent Flows using Deep Learning

Maciej Balajewicz, University of Illinois at Urbana-Champaign

Usage Details

Computational models of high-dimensional, complex dynamical systems arise in a number of applications such as in turbulence modeling or global economic forecasting. Unfortunately, high-fidelity numerical simulations of these applications are often computationally prohibitive for parametric and time-critical applications such as design, optimization, and control. Traditional methods of model reduction aim to reduce this computational burden by capturing subspaces, usually obtained through, e.g., proper orthogonal decomposition, that optimally describe the spatio-temporal dynamics and projecting the governing equations onto these subspaces to get a low-dimensional evolution equation. Here, we propose to leverage the recent advancements in deep learning, in particular sequence-to-sequence models, to develop a framework for purely data-driven model reduction. In this framework, spatio-temporal solution data from a complex dynamical system are used to train a sequence-to-sequence model, whose goal is to generate a sequence of low-dimensional representations of the original high-dimensional system. This approach is similar to current neural machine translation (NMT) models in which sentences from one language are mapped to sentences in a different language. However, similar to NMT, training this model is highly data-intensive and can only be feasible through the use of Blue Waters' petascale resources and graphical processing units. The two main objectives of this exploratory project are to bring our existing code to full scale deployment and to demonstrate the feasibility of our approach.