Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures

TL;DR

This paper introduces a deep learning-based reduced order model that efficiently simulates complex nonlinear microstructure dynamics in real-time, combining autoencoders and neural networks trained on high-fidelity data.

Contribution

It presents a novel non-intrusive DL-ROM framework that integrates POD-Galerkin methods with deep autoencoders and neural networks for real-time nonlinear system simulation.

Findings

Achieves significant computational speed-up over high-fidelity models.

Successfully models nonlinear dynamics of microstructures like micromirrors.

Demonstrates real-time performance in complex system simulations.

Abstract

We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity snapshots are used to generate a POD-Galerkin ROM which is subsequently exploited to generate the data, covering the whole parameter range, used in the training phase of the DL-ROM. A convolutional autoencoder is employed to map the system response onto a low-dimensional representation and, in parallel, to model the reduced nonlinear trial manifold. The system dynamics on the manifold is described by means of a deep feedforward neural network that is trained together with the autoencoder. The strategy is benchmarked against high fidelity solutions on a clamped-clamped beam and on a real micromirror with softening response and multiplicity of solutions. By comparing the different computational costs, we discuss the impressive gain in performance and show that the DL-ROM truly represents a real-time tool which can be profitably and efficiently employed in complex system-level simulation procedures for design and optimisation purposes.