Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator applications has thus far been data-driven, which neglects the intrinsic preservation of fundamental physical laws in data. In this paper, we introduce a novel integral neural operator architecture, to learn physical models with fundamental conservation laws automatically guaranteed. In particular, by replacing the frame-dependent position information with its invariant counterpart in the kernel space, the proposed neural operator is by design translation- and rotation-invariant, and consequently abides by the conservation laws of linear and angular momentums. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental datasets, and show that, by automatically satisfying these essential physical laws, our learned neural operator is not only generalizable in handling translated and rotated datasets, but also achieves state-of-the-art accuracy and efficiency as compared to baseline neural operator models.
翻译:作为隐性治理方程式的隐含解决方案操作者,神经操作者最近已成为学习复杂现实物理系统反应的常用工具,然而,大多数神经操作者应用迄今为止都是由数据驱动的,这忽视了数据中基本物理法的内在保护。在本文中,我们引入了一个新的整体神经操作者结构,以基本保护法自动保障的方式学习物理模型。特别是,拟议的神经操作者通过在核心空间中以其无变动的对应方取代依赖框架的定位信息,通过设计翻译和旋转变换,从而遵守线性和角动力的保存法。作为应用,我们展示了我们在从合成和实验数据集中学习复杂材料行为的模型的清晰性和有效性,并表明,通过自动满足这些基本物理法则,我们所学的神经操作者不仅能够处理翻译和旋转数据集,而且能够实现与基线神经操作者模型相比的状态准确性和效率。