Mechanical MNIST: A benchmark dataset for mechanical metamodels

Metamodels, or models of models, map defined model inputs to defined model outputs. Typically, metamodels are constructed by generating a dataset through sampling a direct model and training a machine learning algorithm to predict a limited number of model outputs from varying model inputs. When metamodels are constructed to be computationally cheap, they are an invaluable 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 a benchmark data set (Mechanical MNIST) for constructing metamodels of heterogeneous material undergoing large deformation. We then show examples of how our benchmark dataset can be used, and establish baseline metamodel performance. Because our dataset is readily available, it will enable the direct quantitative comparison between different metamodeling approaches in a pragmatic manner. We anticipate that it 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.Accepted manuscrip

FM-track: a fiducial marker tracking software for studying cell mechanics in a three-dimensional environment

Tracking the deformation of fiducial markers in the vicinity of living cells embedded in compliant synthetic or biological gels is a powerful means to study cell mechanics and mechanobiology in three-dimensional environments. However, current approaches to track and quantify three-dimensional (3D) fiducial marker displacements remain ad-hoc, can be difficult to implement, and may not produce reliable results. Herein, we present a compact software package entitled “FM-Track,” written in the popular Python language, to facilitate feature-based particle tracking tailored for 3D cell micromechanical environment studies. FM-Track contains functions for pre-processing images, running fiducial marker tracking, and post-processing and visualization. FM-Track can thus aid the study of cellular mechanics and mechanobiology by providing an extensible software platform to more reliably extract complex local 3D cell contractile information in transparent compliant gel systems.https://www.sciencedirect.com/science/article/pii/S2352711019303474Published versio

Locality sensitive hashing via mechanical behavior

From healing wounds to maintaining homeostasis in cyclically loaded tissue, living systems have a phenomenal ability to sense, store, and respond to mechanical stimuli. Broadly speaking, there is significant interest in designing engineered systems to recapitulate this incredible functionality. In engineered systems, we have seen significant recent computationally driven advances in sensing and control. And, there has been a growing interest - inspired in part by the incredible distributed and emergent functionality observed in the natural world - in exploring the ability of engineered systems to perform computation through mechanisms that are fundamentally driven by physical laws. In this work, we focus on a small segment of this broad and evolving field: locality sensitive hashing via mechanical behavior. Specifically, we will address the question: can mechanical information (i.e., loads) be transformed by mechanical systems (i.e., converted into sensor readouts) such that the mechanical system meets the requirements for a locality sensitive hash function? Overall, we not only find that mechanical systems are able to perform this function, but also that different mechanical systems vary widely in their efficacy at this task. Looking forward, we view this work as a starting point for significant future investigation into the design and optimization of mechanical systems for conveying mechanical information for downstream computing.Comment: 20 pages, 9 figures, 1 tabl

Investigating Deep Learning Model Calibration for Classification Problems in Mechanics

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.Comment: 21 pages, 9 figure

Predicting mechanically driven full-field quantities of interest with deep learning-based metamodels

Using simulation to predict the mechanical behavior of heterogeneous materials has applications ranging from topology optimization to multi-scale structural analysis. However, full-fidelity simulation techniques such as Finite Element Analysis, while effective, can be prohibitively computationally expensive when they are used to explore the massive input parameter space of heterogeneous materials. Therefore, there has been significant recent interest in machine learning-based models that, once trained, can predict mechanical behavior at a fraction of the computational cost compared to full fidelity simulations. Over the past several years, research in this area has been focused mainly on predicting single Quantities of Interest (QoIs). However, there has recently been an increased interest in a more challenging problem: predicting full-field QoI (e.g., displacement/strain fields, damage fields) for mechanical problems. Due to the added complexity of full-field information, network architectures that perform well on single QoI problems may perform relatively poorly in the full-field QoI problem setting. This problem is also challenging because, even outside the Mechanics research community, deep learning approaches to image-to-image mapping and full-field image analysis remain poorly understood. The work presented in this paper is twofold. First, we made a significant extension to the Mechanical MNIST dataset designed to enable the investigation of full-field QoI prediction. Specifically, we added Finite Element simulation results of quasi-static brittle fracture in a heterogeneous material captured with the phase-field method. This problem was chosen as a broadly relevant ”challenge problem” for full-field QoI prediction. Second, we investigated multiple Deep Neural Network architectures and subsequently established strong baseline performance for predicting full-field QoI. We found that a MultiRes-WNet architecture with straightforward data augmentation achieves 0.80% and 0.34% Mean Absolute Percentage Error on full-field displacement prediction for Equibiaxial Extension and Uniaxial Extension datasets in the Mechanical MNIST Fashion dataset, respectively. In addition, we found that our MultiRes-WNet architecture combined with a basic Convolutional Autoencoder achieves a mean score of 0.87 on the newly added Mechanical MNIST Crack Path dataset. In addition to presenting the results in this paper, we have released our model implementation and the Mechanical MNIST Crack Path dataset under open-source licenses. We anticipate that future researchers will directly use our model architecture on related datasets and potentially design models that exceed the baseline performance for predicting full-field QoI established in this paper.Accepted manuscrip

Mechanical MNIST – Unsupervised Learning Dataset

The paper “Segmenting Mechanically Heterogeneous Domain via Unsupervised Learning” can be found at . All code necessary to reproduce these finite element simulations and the results in the paper is available on GitHub (https://github.com/quan4444/cluster_project). For questions, please contact Emma Lejeune ([email protected]).The Mechanical MNIST dataset collection contains Finite Element simulations of heterogeneous materials undergoing applied displacement. Here, we introduce a new benchmark dataset designed specifically for assessing unsupervised learning methods where the goal is to discover patterns from unlabeled data. To obtain this dataset, we generate displacement fields from Finite Element simulations and uniformly sample approximately 1500 displacement markers on each domain of interest. Since unsupervised learning aims to identify patterns in labeled data, we provide a dataset where the primary objective is to explore unlabeled data, while simultaneously providing “ground truth” information to ultimately evaluate the efficacy of different unsupervised learning approaches. It is important to note however, that in the intended applications of these methods, ground truth information will likely be absent, particularly in experimental studies of intricate heterogeneous soft tissue. Broadly speaking, this computationally generated dataset mimics the behavior of soft materials, while simultaneously providing ground truth information for method evaluation. In total, the dataset contains the following combinations of conditions: 6 different heterogeneous material patterns, 2 constitutive models, 4 controlled boundary conditions, and 1 random boundary condition. Here, we include the tutorials for our dataset with the name “dataset_tutorials.pdf”. This document contains the information to understand the contents of our dataset, as well as the instructions on how to use the data. The many options from our dataset should enable researchers to explore unsupervised learning methods on soft materials

Exploring the potential of transfer learning for metamodels of heterogeneous material deformation

From the nano-scale to the macro-scale, biological tissue is spatially heterogeneous. Even when tissue behavior is well understood, the exact subject specific spatial distribution of material properties is often unknown. And, when developing computational models of biological tissue, it is usually prohibitively computationally expensive to simulate every plausible spatial distribution of material properties for each problem of interest. Therefore, one of the major challenges in developing accurate computational models of biological tissue is capturing the potential effects of this spatial heterogeneity. Recently, machine learning based metamodels have gained popularity as a computationally tractable way to overcome this problem because they can make predictions based on a limited number of direct simulation runs. These metamodels are promising, but they often still require a high number of direct simulations to achieve an acceptable performance. Here we show that transfer learning, a strategy where knowledge gained while solving one problem is transferred to solving a different but related problem, can help overcome this limitation. Critically, transfer learning can be used to leverage both low-fidelity simulation data and simulation data that is the outcome of solving a different but related mechanical problem. In this paper, we extend Mechanical MNIST, our open source benchmark dataset of heterogeneous material undergoing large deformation, to include a selection of low-fidelity simulation results that require ≈ 2 - 4 orders of magnitude less CPU time to run. Then, we show that transferring the knowledge stored in metamodels trained on these low-fidelity simulation results can vastly improve the performance of metamodels used to predict the results of high-fidelity simulations. In the most dramatic examples, metamodels trained on 100 high fidelity simulations but pre-trained on 60,000 low-fidelity simulations achieves nearly the same test error as metamodels trained on 60,000 high-fidelity simulations (1 - 1.5% mean absolute percent error). In addition, we show that transfer learning is an effective method for leveraging data from different load cases, and for leveraging low-fidelity two-dimensional simulations to predict the outcomes of high-fidelity three-dimensional simulations. Looking forward, we anticipate that transfer learning will enable us to better capture the influence of tissue spatial heterogeneity on the mechanical behavior of biological materials across multiple different domains.First author draf

Towards out of distribution generalization for problems in mechanics

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Sarc-Graph: automated segmentation, tracking, and analysis of sarcomeres in hiPSC-derived cardiomyocytes

A better fundamental understanding of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) has the potential to advance applications ranging from drug discovery to cardiac repair. Automated quantitative analysis of beating hiPSC-CMs is an important and fast developing component of the hiPSC-CM research pipeline. Here we introduce "Sarc-Graph," a computational framework to segment, track, and analyze sarcomeres in fluorescently tagged hiPSC-CMs. Our framework includes functions to segment z-discs and sarcomeres, track z-discs and sarcomeres in beating cells, and perform automated spatiotemporal analysis and data visualization. In addition to reporting good performance for sarcomere segmentation and tracking with little to no parameter tuning and a short runtime, we introduce two novel analysis approaches. First, we construct spatial graphs where z-discs correspond to nodes and sarcomeres correspond to edges. This makes measuring the network distance between each sarcomere (i.e., the number of connecting sarcomeres separating each sarcomere pair) straightforward. Second, we treat tracked and segmented components as fiducial markers and use them to compute the approximate deformation gradient of the entire tracked population. This represents a new quantitative descriptor of hiPSC-CM function. We showcase and validate our approach with both synthetic and experimental movies of beating hiPSC-CMs. By publishing Sarc-Graph, we aim to make automated quantitative analysis of hiPSC-CM behavior more accessible to the broader research community.https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1009443Published versio

A Data-Driven Computational Model for Engineered Cardiac Microtissues

Engineered heart tissues (EHTs) present a potential solution to some of the current challenges in the treatment of heart disease; however, the development of mature, adult-like cardiac tissues remains elusive. Mechanical stimuli have been observed to improve whole-tissue function and cardiomyocyte (CM) maturation, although our ability to fully utilize these mechanisms is hampered, in part, by our incomplete understanding of the mechanobiology of EHTs. In this work, we leverage the experimental data produced by a mechanically tunable experimental setup to generate tissue-specific computational models of EHTs. Using imaging and functional data, our modeling pipeline generates models with tissue-specific ECM and myofibril structure, allowing us to estimate CM active stress. We use this experimental and modeling pipeline to study different mechanical environments, where we contrast the force output of the tissue with the computed active stress of CMs. We show that the significant differences in measured experimental forces can largely be explained by the levels of myofibril formation achieved by the CMs in the distinct mechanical environments, with active stress showing more muted variations across conditions. The presented model also enables us to dissect the relative contributions of myofibrils and extracellular matrix to tissue force output, a task difficult to address experimentally. These results highlight the importance of tissue-specific modeling to augment EHT experiments, providing deeper insights into the mechanobiology driving EHT function.Comment: 19 pages, 7 figure