Saeed Mohammadzadeh

Hiba Kobeissi, Saeed Mohammadzadeh, Emma Lejeune

Modeling biological soft tissue is complex in part due to material heterogeneity. Microstructural patterns, which play a major role in defining the mechanical behavior of these tissues, are both challenging to characterize, and difficult to simulate. Recently, machine learning-based methods to predict the mechanical behavior of heterogeneous materials have made it possible to more thoroughly explore the massive input parameter space associated with heterogeneous blocks of material. Specifically, we can train machine learning (ML) models to closely approximate computationally expensive heterogeneous material simulations where the ML model is trained on a dataset of simulations that capture the range of spatial heterogeneity present in the material of interest. However, when it comes to applying these techniques to biological tissue more broadly, there is a major limitation: the relevant microstructural patterns are both challenging to obtain and difficult to analyze. Consequently, the number of useful examples available to characterize the input domain under study is limited. In this work, we investigate the efficacy of ML-based generative models as well as procedural methods as a tool for augmenting limited input pattern datasets. We find that a Style-based Generative Adversarial Network with adaptive discriminator augmentation is able to successfully leverage just 1,000 example patterns to create the most authentic generated patterns. In general, diverse generated patterns with adequate resemblance to the real patterns can be used as inputs to finite element simulations to meaningfully augment the training dataset. To enable this methodological contribution, we have created an open access dataset of Finite Element Analysis simulations based on Cahn-Hilliard patterns. We anticipate that future researchers will be able to leverage this dataset and build on the work presented here.

Saeed Mohammadzadeh, Peerasait Prachaseree, Emma Lejeune

Recently, there has been a growing interest in applying machine learning methods to problems in engineering mechanics. In particular, there has been significant interest in applying deep learning techniques to predicting the mechanical behavior of heterogeneous materials and structures. Researchers have shown that deep learning methods are able to effectively predict mechanical behavior with low error for systems ranging from engineered composites, to geometrically complex metamaterials, to heterogeneous biological tissue. However, there has been comparatively little attention paid to deep learning model calibration, i.e., the match between predicted probabilities of outcomes and the true probabilities of outcomes. In this work, we perform a comprehensive investigation into ML model calibration across seven open access engineering mechanics datasets that cover three distinct types of mechanical problems. Specifically, we evaluate both model and model calibration error for multiple machine learning methods, and investigate the influence of ensemble averaging and post hoc model calibration via temperature scaling. Overall, we find that ensemble averaging of deep neural networks is both an effective and consistent tool for improving model calibration, while temperature scaling has comparatively limited benefits. Looking forward, we anticipate that this investigation will lay the foundation for future work in developing mechanics specific approaches to deep learning model calibration.