INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservation-猫眼课题宝

DOI：

10.48550/arxiv.2212.14365

发表时间：

2022-12

期刊：

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通讯作者：

中科院分区：

其他

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作者：

Ning Liu;Yue Yu;Huaiqian You;Neeraj Tatikola

神经操作符，出现作为隐式控制方程的解决方案运营商，最近成为流行的工具，学习复杂的现实世界的物理系统的响应。然而，到目前为止，大多数神经运算符应用都是数据驱动的，这忽略了数据中基本物理定律的内在保持。在本文中，我们介绍了一种新的积分神经操作符架构，学习物理模型的基本守恒律自动保证。特别是，通过用其在核空间中的不变对应物替换依赖于帧的位置信息，所提出的神经算子通过设计是平移和旋转不变的，因此遵守线性和角动量的守恒定律。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有效性，并表明，通过自动满足这些基本物理定律，我们学习的神经运算符不仅在处理平移和旋转数据集时是可推广的，而且与基线神经运算符模型相比，还实现了最先进的准确性和效率。

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.

INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservation

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