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Highly nonlinear dynamic finite element simulations using explicit time integration are particularly valuable tools for structural analysis in fields like automotive, aerospace, and civil engineering, or in the study of injury biomechanics. However, such state-of-the-art simulation models demand significant computational resources. Conventional data-driven surrogate modeling approaches address this by evolving the dynamics on low-dimensional embeddings, yet the majority of them operate directly on high-resolution data obtained from numerical discretizations, making them costly and unsuitable for adaptive resolutions or for handling information flow over large spatial distances. We therefore propose a multi-hierarchical framework for the structured creation of a series of surrogate models at different resolutions. Macroscale features are captured on coarse surrogates, while microscale effects are resolved on finer ones, while leveraging transfer learning to pass information between scales. The objective of this study is to develop efficient surrogates for a kart frame model in a frontal impact scenario. To achieve this, its mesh is simplified to obtain multi-resolution representations of the kart. Subsequently, a graph-convolutional neural network-based surrogate learns parameter-dependent low-dimensional latent dynamics on the coarsest representation. Following surrogates are trained on residuals using finer resolutions, allowing for multiple surrogates with varying hardware requirements and increasing accuracy.

Quantitative phase imaging (QPI) recovers the exact wavefront of light from intensity measurements. Topographical and optical density maps of translucent microscopic bodies can be extracted from these quantified phase shifts. We demonstrate quantitative phase imaging at the tip of a coherent fiber bundle using chromatic aberrations inherent in a silicon nitride hyperboloid metalens. Our method leverages spectral multiplexing to recover phase from multiple defocus planes in a single capture using a color camera. Our 0.5 mm aperture metalens shows robust quantitative phase imaging capability with a$${28}^{\circ}$$${28}^{\circ }$field of view and 0.$${2}{\pi}$$$2\pi$phase resolution ( ~ 0.$${1}{\lambda}$$$1\lambda$in air) for experiments with an endoscopic fiber bundle. Since the spectral functionality is encoded directly in the imaging lens, the metalens acts both as a focusing element and a spectral filter. The use of a simple computational backend will enable real-time operation. Key limitations in the adoption of phase imaging methods for endoscopy such as multiple acquisition, interferometric alignment or mechanical scanning are completely mitigated in the reported metalens based QPI.