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

66/2023

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

Tuesday 5th September 2023

Fresca, S.; Gobat, G.; Fedeli, P.; Frangi, A.; Manzoni, A.

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.

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S. Fresca, G. Gobat, P. Fedeli, A. Frangi, A. Manzoni. Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures, Int. J. Numer. Meth. Engng. 123 (20): 4749-4777, 2022