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.

中文翻译：

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通过基于深度学习的降阶模型实时模拟参数相关的流体流动

在不同的虚拟场景中模拟流体流动在工程应用中至关重要。然而，当必须几乎实时地模拟流体流动时，依靠（例如）有限元方法的高保真全阶模型是负担不起的。例如，依赖于适当正交分解 (POD) 的降阶模型 (ROM) 可以快速提供对依赖于参数的流体动力学问题的可靠近似。然而，如果考虑混合速度-压力公式，它们可能需要昂贵的超缩减策略来处理参数化非线性项，并丰富缩减空间（或 Petrov-Galerkin 投影），这可能会妨碍对可靠解决方案的实时评估。处理流固耦合带来更高的困难。所提出的基于深度学习 (DL) 的 ROM 通过以非侵入性方式学习非线性试验流形和减少的动力学，克服了所有这些限制。为此，他们依靠深度神经网络，在通过 POD 执行以前的降维之后，大大提高了他们的训练时间。结果表明，生成的 POD-DL-ROM 几乎可以实时提供围绕圆柱基准的流动的准确结果，连接到固定刚性块的弹性梁与不可压缩层流之间的流固耦合，以及脑动脉瘤中的血流。在通过 POD 执行以前的降维之后，他们的训练时间大大增加。结果表明，生成的 POD-DL-ROM 几乎可以实时提供围绕圆柱基准的流动的准确结果，连接到固定刚性块的弹性梁与不可压缩层流之间的流固耦合，以及脑动脉瘤中的血流。在通过 POD 执行以前的降维之后，他们的训练时间大大增加。结果表明，生成的 POD-DL-ROM 几乎可以实时提供围绕圆柱基准的流动的准确结果，连接到固定刚性块的弹性梁与不可压缩层流之间的流固耦合，以及脑动脉瘤中的血流。