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

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 optimization purposes.