Computer Vision with Error Estimation for Reduced Order Modeling of Macroscopic Mechanical Tests

Abstract

In this paper, computer vision enables recommending a reduced order model for fast stress prediction according to various possible loading environments. This approach is applied on a macroscopic part by using a digital image of a mechanical test. We propose a hybrid approach that simultaneously exploits a data-driven model and a physics-based model, in mechanics of materials. During a machine learning stage, a classification of possible reduced order models is obtained through a clustering of loading environments by using simulation data. The recognition of the suitable reduced order model is performed via a convolutional neural network (CNN) applied to a digital image of the mechanical test. The CNN recommend a convenient mechanical model available in a dictionary of reduced order models. The output of the convolutional neural network being a model, an error estimator, is proposed to assess the accuracy of this output. This article details simple algorithmic choices that allowed a realistic mechanical modeling via computer vision.

Model order reduction assisted by deep neural networks (ROM-net)

“…Definition 4 (Dictionary-based ROM-net) Let us consider a physics problem, where a quantity of interest Y ∈ Y depends on a tensorial input variable X ∈ X and can be predicted by a reduced-order solver S : Figure 2 illustrates the concept of dictionary-based ROM-nets. The strategy presented in [31] for image-based modeling using convolutional neural networks and a dictionary of local reduced-order models fits the definition of a dictionary-based ROM-net. In this definition, the expression deep classifier denotes deep neural networks returning a single class label in [[1; K ]] for a given tensorial input.…”

“…In [30], a nonlinear dimensionality reduction is performed using deep convolutional autoencoders. The modeling strategy presented in [31] was the first hybrid approach involving both a dictionary of local hyperreduced-order models and computer vision techniques. In the context of image-based modeling, it showed that convolutional neural networks could be used to recognize the loading case of a mechanical experiment on a digital image, and select a suitable hyperreduced-order model to simulate the experiment.…”

“…Dictionary-based ROM-nets can be made of one or several deep neural networks selecting the best reducedorder model from a dictionary. In our case, unlike the strategy presented in [31], this dictionary derives from the clustering of outputs of simplified simulations using distances on a Grassmannian. In the first section of this article, we introduce the formal definitions of ROM-nets and dictionary-based ROM-nets.…”

Mechanical dissimilarity of defects in welded joints via Grassmann manifold and machine learning

“…These networks are no longer used as projection-based model order reduction schemes. However, such reduced schemes are found in [25] and [22], where a deep classifier recommends a reduced order model depending on input variables having a tensor format (e.g., images). In [25], a CNN recommends a reduced order model related to a loading environment seen on the image of an experimental setup.…”

“…However, such reduced schemes are found in [25] and [22], where a deep classifier recommends a reduced order model depending on input variables having a tensor format (e.g., images). In [25], a CNN recommends a reduced order model related to a loading environment seen on the image of an experimental setup. In [22], a deep classifier using CNN is trained to recommend hyperreduced order models for lifetime prediction depending on a three-dimensional (3D) stochastic temperature field.…”