Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neural operator applications have thus far been data-driven and neglect the intrinsic preservation of fundamental physical laws in data. In this work, we introduce a novel integral neural operator architecture called the Peridynamic Neural Operator (PNO) that learns a nonlocal constitutive law from data. This neural operator provides a forward model in the form of state-based peridynamics, with objectivity and momentum balance laws automatically guaranteed. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental data sets. We also compare the performances with baseline models that use predefined constitutive laws. We show that, owing to its ability to capture complex responses, our learned neural operator achieves improved accuracy and efficiency. Moreover, by preserving the essential physical laws within the neural network architecture, the PNO is robust in treating noisy data. The method shows generalizability to different domain configurations, external loadings, and discretizations.

中文翻译：

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近场动力学神经算子：复杂材料响应的数据驱动的非局部本构模型

神经算子可以充当隐藏控制方程的隐式解算子，最近已成为学习复杂现实世界物理系统响应的流行工具。然而，迄今为止，大多数神经算子应用都是数据驱动的，忽略了数据中基本物理定律的内在保存。在这项工作中，我们引入了一种称为近场动力学神经算子（PNO）的新型积分神经算子架构，它从数据中学习非局部本构律。该神经算子提供了基于状态的近场动力学形式的正演模型，自动保证了客观性和动量平衡定律。作为应用，我们展示了我们的模型在从合成和实验数据集学习复杂材料行为方面的表现力和功效。我们还将性能与使用预定义本构定律的基线模型进行了比较。我们表明，由于我们学习的神经算子能够捕获复杂的响应，因此可以提高准确性和效率。此外，通过保留神经网络架构内的基本物理定律，PNO 在处理噪声数据方面具有鲁棒性。该方法显示了对不同域配置、外部载荷和离散化的通用性。