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

TL;DR

This paper introduces deep learning-based reduced order models that enable fast, accurate, and non-intrusive simulation of parameter-dependent fluid flows, overcoming limitations of traditional methods especially in complex scenarios.

Contribution

It presents a novel POD-DL-ROM approach that learns nonlinear trial manifolds and reduced dynamics using deep neural networks, significantly improving real-time simulation capabilities.

Findings

Accurate flow simulations around a cylinder in near real-time.

Effective fluid-structure interaction modeling with deep learning.

Successful blood flow simulation in cerebral aneurysm.

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.