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

• URL: http://arxiv.org/abs/2106.05722v1
• Date: Thu, 10 Jun 2021 13:07:33 GMT
• Title: Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models
• Authors: Stefania Fresca, Andrea Manzoni
• Abstract summary: Reduced order models (ROMs) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. 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. 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.
• Score: 0.2538209532048866
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 real-time. 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.

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