Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models

Abstract

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. However, they might require expensive hyper-reduction strategies for handling parameterized nonlinear terms, and enriched reduced spaces (or Petrov-Galerkin projections) if a mixed velocity-pressure formulation is considered, possibly hampering the evaluation of reliable solutions in realtime. Dealing with fluid-structure interactions entails even higher difficulties. The proposed deep learning (DL)-based ROMs overcome all these limitations by learning in a non-intrusive way both the nonlinear trial manifold and the reduced dynamics. To do so, they rely on deep neural networks, after performing a former dimensionality reduction through POD enhancing their training times substantially. The resulting POD-DL-ROMs are shown to provide accurate results in almost real-time for the flow around a cylinder benchmark, the fluid-structure interaction between an elastic beam attached to a fixed, rigid block and a laminar incompressible flow, and the blood flow in a cerebral aneurysm.

Reduced order modelling for direct and inverse problems in haemodynamics

“…In (Koeppl et al, 2018) a database of 1-D reduced models on a systemic network is build and a surrogate model based on kernel methods is proposed in order to perform a real time simulation of the global circulation. In (Fresca and Manzoni, 2021) a method based on deep learning is proposed to speed up the approximation of blood flow. In this work, the authors perform, first, a POD basis extraction, whose goal is to reduce the training phase cost.…”

Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

“…Such hybrid architectures consider spatio-temporal domain knowledge and achieve data-driven time series predictions. Recently proposed POD-based DL-ROMs are the POD-CNN by Miyanawala and Jaiman 40 , the POD-RNN by Bukka et al 7 , the POD-enhanced autoencoders by Fresca and Manzoni 17 . These hybrid architectures have been demonstrated for 2D bluff body flows with and without fluid-structure interaction.…”

“…Likewise, Snachez et al 51 and Pfaff et al 46 utilized graph neural networks to represent the state of a physical system as nodes in a graph and compute the dynamics by learning messagepassing signals. The third category in the physics-based deep learning involves the development of the hybrid DL-ROMs that take into account the spatial and temporal domain knowledge in neural networks 7,17,19,40 . We refer to such DL-ROM frameworks as physics-based because they incorporate physical interpretability via proper orthogonal decomposition and its variants.…”

“…In this paper, we develop a deep learning-based reduced-order modeling framework for (a) three-dimensional unsteady flow predictions, (b) parametric flow and force predictions with variable Reynolds number, and (c) data-driven computational speed-ups for both offline training and online prediction of complex 3D wake flow. Although there are a few studies that use CNNs and autoencoder for parametric dependent flow problems 17,34 , there is no work that attempts to develop a DL-ROM methodology for the flow past 3D geometries in a way that can provide an effective mean to couple with real-time flow field snapshots 35,48 .…”