Learning Mechanically Driven Emergent Behavior with Message Passing Neural Networks
Learning Mechanically Driven Emergent Behavior with Message Passing Neural Networks
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DOI：
10.1016/j.compstruc.2022.106825
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发表时间：
2022-02
期刊：
影响因子：
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通讯作者：
Peerasait Prachaseree;E. Lejeune
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文献类型：
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作者：
Peerasait Prachaseree;E. Lejeune
从设计结构材料到跨尺度连接机械行为，计算建模是理解和预测可变形体机械响应的关键工具。特别是，计算建模是一个宝贵的工具，用于预测全球涌现的现象，如几何不稳定性的发作，或异质性诱导的对称性破缺。最近，人们越来越关注使用基于机器学习的计算模型直接从实验数据中学习机械行为，以及使用机器学习（ML）方法来降低基于物理的模拟的计算成本。值得注意的是，依赖于图神经网络（GNN）的机器学习方法最近已被证明可以在基于粒子和基于网格的模拟的多个示例中有效地预测机械行为。然而，尽管这最初的承诺，性能的图形为基础的方法还有待调查的无数固体力学问题。在这项工作中，我们研究了神经信息传递的能力，以预测机械驱动的紧急行为的一个基本方面：一个列的几何结构和方向之间的连接，它所包含的。为了实现这一点，我们引入了非对称屈曲柱（ABC）数据集，该数据集由三种类型的非对称和异质柱几何形状（子数据集1，子数据集2和子数据集3）组成，其目标是在屈曲不稳定性发生后对压缩下的对称性破坏方向（左或右）进行分类。值得注意的是，对于典型的ML方法，很难将这些结构参数化为特征向量。本质上，因为这些列的几何形状是不连续和复杂的，所以局部几何图案将被实现基于卷积神经网络的元模型所需的低分辨率“图像状”数据表示扭曲。相反，我们提出了一个管道来学习全局紧急属性，同时使用消息传递神经网络执行局部性。具体来说，我们从计算机视觉研究领域基于点云的分类问题中汲取灵感，并使用PointNet++层对ABC数据集进行分类。除了研究GNN模型架构外，我们还研究了不同输入数据表示方法，数据增强以及将多个模型组合为一个整体的效果。总的来说，我们能够使用这种方法实现良好的性能，从子数据集1的0.952预测准确度到子数据集2的0.913预测准确度，再到子数据集3的0.856预测准确度，每个训练数据集大小为20，000点。然而，这些结果也清楚地表明，用这些方法预测基于固体力学的涌现行为是不平凡的。由于我们的模型实现和数据集都是在开源许可证下分发的，我们希望未来的研究人员可以在我们的工作基础上创建增强的特定于机制的机器学习方法。此外，我们还打算在将机器学习应用于力学研究时，围绕表示复杂机械结构的不同方法展开讨论。
From designing architected materials to connecting mechanical behavior across scales, computational modeling is a critical tool for understanding and predicting the mechanical response of deformable bodies. In particular, computational modeling is an invaluable tool for predicting global emergent phenomena, such as the onset of geometric instabilities, or heterogeneity induced symmetry breaking. Recently, there has been a growing interest in both using machine learning based computational models to learn mechanical behavior directly from experimental data, and using machine learning (ML) methods to reduce the computational cost of physics-based simulations. Notably, machine learning approaches that rely on Graph Neural Networks (GNNs) have recently been shown to effectively predict mechanical behavior in multiple examples of particle-based and mesh-based simulations. However, despite this initial promise, the performance of graph based methods have yet to be investigated on a myriad of solid mechanics problems. In this work, we examine the ability of neural message passing to predict a fundamental aspect of mechanically driven emergent behavior: the connection between a column’s geometric structure and the direction that it buckles. To accomplish this, we introduce the Asymmetric Buckling Columns (ABC) dataset, a dataset comprised of three types of asymmetric and heterogeneous column geometries (sub-dataset 1, sub-dataset 2, and sub-dataset 3) where the goal is to classify the direction of symmetry breaking (left or right) under compression after the onset of the buckling instability. Notably, it is difficult to parameterize these structures into a feature vector for typical ML methods. Essentially, because the geometry of these columns is discontinuous and intricate, local geometric patterns will be distorted by the low-resolution “image-like” data representations that are required to implement convolutional neural network based metamodels. Instead, we present a pipeline to learn global emergent properties while enforcing locality with message passing neural networks. Specifically, we take inspiration from point cloud based classification problems from the computer vision research field and use PointNet++ layers to perform classification on the ABC dataset. In addition to investigating GNN model architecture, we study the effect of different input data representation approaches, data augmentation, and combining multiple models as an ensemble. Overall, we were able to achieve good performance with this approach, ranging from 0.952 prediction accuracy on sub-dataset 1, to 0.913 prediction accuracy on sub-dataset 2, to 0.856 prediction accuracy on sub-dataset 3 for training dataset sizes of 20, 000 points each. However, these results also clearly indicate that predicting solid mechanics based emergent behavior with these methods is non-trivial. Because both our model implementation and dataset are distributed under open-source licenses, we hope that future researchers can build on our work to create enhanced mechanics-specific machine learning methods. Furthermore, we also intend to provoke discussion around different methods for representing complex mechanical structures when applying machine learning to mechanics research.