Intrusive, Non-intrusive and Hybrid ROM
Research Title: Development of robust intrusive, non-intrusive, and hybrid reduced-order modeling algorithms for nonlinear and chaotic systems using physics-based and data-driven modeling techniques.
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Supervisor: Dr. Omer San, Oklahoma State University.
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Goal: In this project, we put an effort to develop efficient and improved reduced-order models (ROMs) capable of doing real-time simulation for advanced technologies like digital twins and smart manufacturing by integrating existing physics-based ROMs and data-driven tools/machine learning algorithms.
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Summary: We worked on both physics-based and data-driven approaches to develop an improved ROM framework for our test problems. Below a brief description of the progress we made in this research objectives:
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Physics-based intrusive ROM: In this approach, we consider the analogy between Large Eddy Simulation (LES) and truncated modal projection of projection-based ROMs. Since instabilities due to the truncation of modes for multi-scale and large-scale systems is one of the main reasons the conventional projection-based ROM methods fall short, we propose an eddy viscosity closure approach to stabilize the resulting surrogate model. Our efforts, in particular, include the translation of the dynamic subgrid-scale model into our ROM setting by defining a test truncation similar to the test filtering in LES.
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Figure: Closure modeling analogy between large eddy simulation (left) and reduced-order modeling (right). For details, please refer to Rahman et al., 2019a.
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Fully non-intrusive data-driven ROM: We developed a fully data-driven ROM framework for large-scale Quasi-Geostrophic systems which exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the high-resolution data snapshots using POD transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. The mean flow fields and time-series response of the field values are then reconstructed from the predicted modal coefficients by using an inverse POD transform.
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Figure: Workflow diagram of the proposed fully non-intrusive ROM-LSTM framework. For details, please refer to Rahman et al., 2019b.
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Later, for accurate reduced-order modeling of convective flows, we introduce a long short-term memory (LSTM) neural network architecture together with a principal interval decomposition (PID) framework as an effective partitioning tool for breaking the Kolmogorov barrier. For details, please refer to Ahmed et al., 2019.
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Figure: The proposed non-intrusive principal interval decomposition LSTM framework for unsteady non-ergodic flows.
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In another work in this research direction, we developed various Deep Neural Network (DNN) architectures for data-driven reduced-order modeling of dynamical systems relevant to fluid flow which numerically predict the evolution of dynamical systems by learning from either using discrete state or slope information of the system. The details can be found in Pawar et al., 2019.
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Hybrid ROM: To develop our hybrid analytics ROM algorithms, we utilize the neural network emulators to account for the limitations of the physics-based ROMs. In one paper, we introduce a weighting parameter between the Galerkin projection and Extreme Learning Machine (ELM) Artificial Neural Network (ANN) model for near real-time prediction of mesoscale flows. Interested readers are requested to read the details of this work in Rahman et al., 2018a.
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Figure: Schematic representation of the ELM neural network architecture utilized for the data-driven reduced-order modeling framework in this study.
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We also developed a hybrid analytics model to accelerate incompressible flow solvers in Rahman et al., 2018b. A short and concise representation of the proposed hybrid models is presented in the following poster.
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Sponsor Acknowledgement: This research is a part of the US Department of Energy (DOE) funded project titled "Physics-reinforced Machine Learning Algorithms for Multiscale Closure Model Discovery".
