Fracture parameters play an important role in accurately simulating fracture propagation phenomena, which are highly nonlinear and sensitive to various parameters. The main focus of this paper is to offer different proxy modeling techniques to enable the otherwise computationally extremely expensive Bayesian identification procedure performed with Markov Chain Monte Carlo method. The paper contrasts polynomial chaos methods with machine learning techniques, including deep neural networks, in identification of uncertain fracture parameters. In addition, the application of autoencoders to push the stochastic process of deformations to low-dimensional representation is also analyzed. Two fracture scenarios are proposed for parameter identification: the hole tension test and the four point bending test. The 2D fracture propagation model is based on embedded strong discontinuity method, efficiently capturing complex failure mechanisms in modes I and II. The provided results show the successful identification of fracture parameters, including tensile and shear strength, as well as tensile and shear fracture energy using the different proxy modeling techniques and give explanations on the advantages and disadvantages of using different methods.

中文翻译：

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机器学习和基于 gPC 的代理解决方案在高效贝叶斯识别断裂参数方面的比较


裂缝参数在精确模拟裂缝传播现象中起着重要作用，裂缝传播现象具有高度非线性且对各种参数敏感。本文的主要重点是提供不同的代理建模技术，以实现使用马尔可夫链蒙特卡洛方法执行的计算极其昂贵的贝叶斯识别过程。该论文将多项式混沌方法与机器学习技术（包括深度神经网络）在识别不确定的断裂参数方面进行了对比。此外，还分析了自动编码器将变形的随机过程推向低维表示的应用。提出了两种断裂场景进行参数辨识：孔拉试验和四点弯曲试验。二维裂缝扩展模型基于嵌入式强不连续性方法，可有效捕获模式 I 和 II 中的复杂失效机制。提供的结果表明，使用不同的代理建模技术成功识别了断裂参数，包括拉伸和剪切强度，以及拉伸和剪切断裂能量，并解释了使用不同方法的优缺点。