Metamodels, or models of models, map defined inputs to defined outputs. Typically, metamodels are constructed by generating a dataset through sampling a direct model and training a machine learning algorithm to predict specific model outputs from specific varying model inputs. When metamodels are constructed to be computationally inexpensive, they are a critical tool for applications ranging from topology optimization, to uncertainty quantification, to multi-scale simulation. By nature, a given metamodel will be tailored to a specific dataset. However, the most pragmatic metamodel type and structure will often be general to larger classes of problems. At present, the most pragmatic metamodel selection for dealing with mechanical data has not been thoroughly explored. Drawing inspiration from the benchmark datasets available to the computer vision research community, we introduce two benchmark datasets specific to mechanical data. The first dataset, Mechanical MNIST, is relevant to heterogeneous materials undergoing large deformation. Within the Mechanical MNIST dataset, we also include multiple simulation fidelity levels. The second dataset, Buckling Instability Classification (BIC), is relevant to buckling problems where a heterogeneous column is subject to a fixed level of applied displacement and is classified as either ``Stable'' or ``Unstable.'' We then show examples of how our benchmark datasets can be used, and establish baseline metamodel performance for both regression and classification problems. Then, we demonstrate the potential of transfer learning across the Mechanical MNIST dataset and show how the BIC metamodel is vulnerable to adversarial attacks. Because our datasets are readily available, they will enable direct quantitative comparison between different metamodeling approaches in a pragmatic manner. We anticipate that these datasets will enable the broader community of researchers to develop improved metamodeling techniques for mechanical data that will surpass the baseline performance that we show here. 

Two benchmark datasets for mechanical simulation: Mechanical MNIST and BIC

The Virtual Technical Meeting of the Society of Engineering Science 2020 is the first fully virtual meeting of the SES community to envision and connect during the hiatus created by Covid-19, providing a platform for the exchange of ideas, and to showcase the latest research in the field of engineering science.

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