论文标题
多限制深度操作员网络，用于数据驱动和物理信息的问题
Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems
论文作者
论文摘要
复杂非线性系统的操作员学习在建模多物理和多尺度系统中越来越普遍。但是，培训这样的高维操作员需要从实验或模拟中大量昂贵的高保真数据。在这项工作中，我们提出了一个复合深度运算符网络（DeepOnet），用于学习使用两个具有不同水平的保真度的数据集，以便在没有足够的高保真数据时准确地学习复杂的操作员。此外，我们证明了低保真数据的存在可以改善使用deponets的物理知识学习的预测。我们在各种示例中展示了新的多保真训练，包括使用两种不同的保真度模型对洪堡冰川（Greenland）的冰盖动力学进行建模，并在两种不同的分辨率下使用相同的物理模型。
Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either from experiments or simulations. In this work, we present a composite Deep Operator Network (DeepONet) for learning using two datasets with different levels of fidelity to accurately learn complex operators when sufficient high-fidelity data is not available. Additionally, we demonstrate that the presence of low-fidelity data can improve the predictions of physics-informed learning with DeepONets. We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland, using two different fidelity models and also using the same physical model at two different resolutions.
