论文标题
构成人工神经网络的新家族朝着自动化模型发现
A new family of Constitutive Artificial Neural Networks towards automated model discovery
论文作者
论文摘要
100多年来，化学，物理和材料科学家一直提出竞争构成模型，以最好地表征天然和人造材料对机械负荷的行为。现在，计算机科学提供了通用解决方案：神经网络。神经网络是强大的函数近似器，可以从大数据中学习构型关系，而无需任何基础物理学。然而，经典神经网络忽略了本构模型中的一个世纪研究，违反热力学考虑，并且无法预测训练制度之外的行为。在这里，我们设计了一个新的组成型人工神经网络家族，该家族本质地满足了常见的运动学，热力学和物理约束，同时也可以约束可允许功能的设计空间，即使存在稀疏数据，也可以创建可靠的近似值。我们重新审视了机械师的非线性场理论，并反向工程师网络输入以说明材料客观性，对称性和不可压缩性；网络输出以执行热力学一致性；激活功能可以实现身体合理的限制；以及网络体系结构以确保多凸度。我们证明，这种新的模型是对经典的Neo Hooke，Blatz KO，Mooney Rivlin，Yeoh和Demiray模型的概括，并且网络权重具有明确的物理解释。当接受橡胶的经典基准数据培训时，我们的网络自主选择最佳的本构模型并了解其参数。我们的发现表明，组成型人工神经网络有可能引起本构建模的范式转移，从用户定义的模型选择到自动化模型发现。我们的源代码，数据和示例可在https://github.com/livingmatterlab/cann上找到。
For more than 100 years, chemical, physical, and material scientists have proposed competing constitutive models to best characterize the behavior of natural and man-made materials in response to mechanical loading. Now, computer science offers a universal solution: Neural Networks. Neural Networks are powerful function approximators that can learn constitutive relations from large data without any knowledge of the underlying physics. However, classical Neural Networks ignore a century of research in constitutive modeling, violate thermodynamic considerations, and fail to predict the behavior outside the training regime. Here we design a new family of Constitutive Artificial Neural Networks that inherently satisfy common kinematic, thermodynamic, and physic constraints and, at the same time, constrain the design space of admissible functions to create robust approximators, even in the presence of sparse data. We revisit the non-linear field theories of mechanics and reverse-engineer the network input to account for material objectivity, symmetry, and incompressibility; the network output to enforce thermodynamic consistency; the activation functions to implement physically reasonable restrictions; and the network architecture to ensure polyconvexity. We demonstrate that this new class of models is a generalization of the classical neo Hooke, Blatz Ko, Mooney Rivlin, Yeoh, and Demiray models and that the network weights have a clear physical interpretation. When trained with classical benchmark data for rubber, our network autonomously selects the best constitutive model and learns its parameters. Our findings suggests that Constitutive Artificial Neural Networks have the potential to induce a paradigm shift in constitutive modeling, from user-defined model selection to automated model discovery. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.
