MEAM Seminar: “Open Access Benchmark Datasets and Metamodels for Problems in Mechanics”

Metamodels, or models of models, map defined model inputs to defined model outputs. When metamodels are constructed to be computationally cheap, they are an invaluable tool for applications ranging from topology optimization, to uncertainty quantification, to real-time prediction, to multi-scale simulation. In particular, for heterogeneous materials, metamodels are useful for exploring the influence of the (potentially massive) heterogeneous material property parameter space. 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 — specifically simulations of heterogenous materials — has not been thoroughly explored. In this work, we draw inspiration from the benchmark datasets available to the computer vision research community. These benchmark datasets have both made it feasible to compare different methods for solving the same problem, and inspired new directions for method development. In response, we introduce benchmark datasets for engineering mechanics problems (for example, the Mechanical MNIST Collection https://open.bu.edu/handle/2144/39371 [1,2,3]). Then, we show some example problems that we are exploring with these datasets such as our methodology for constructing metamodels for predicting full field quantities of interest (e.g., full field displacements, stress, strain, or damage variable), and for leveraging information from multiple simulation fidelities, and for predicting out of distribution behavior. Looking forward, we anticipate that disseminating both these benchmark datasets and our computational methods will enable the broader community of researchers to develop improved techniques for understanding the behavior of spatially heterogeneous materials. We also hope to inspire others to use our datasets for educational and research purposes, and to disseminate datasets and metamodels specific to their own areas of interest (https://elejeune11.github.io/).

[1] Lejeune, E. (2020). Mechanical MNIST: A benchmark dataset for mechanical metamodels. Extreme Mechanics Letters, 36, 100659.
[2] Lejeune, E., & Zhao, B. (2020). Exploring the potential of transfer learning for metamodels of heterogeneous material deformation. Journal of the Mechanical Behavior of Biomedical Materials, 104276.
[3] Mohammadzadeh, S., & Lejeune, E. (2022). Predicting mechanically driven full-field quantities of interest with deep learning-based metamodels. Extreme Mechanics Letters, 50, 101566.