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.

翻译：针对复杂非线性系统的算子学习在多物理场和多尺度系统建模中日益普遍。然而，训练此类高维算子需要大量昂贵的、高保真度数据（无论来自实验还是模拟）。本文提出一种复合深度算子网络（DeepONet），利用两种不同保真度水平的数据集进行学习，在缺乏足够高保真度数据时精确获取复杂算子。此外，我们证明低保真度数据的存在可提升基于物理信息的DeepONet学习预测能力。我们通过多个示例验证了这种新型多保真度训练方法，包括使用两种不同保真度模型对格陵兰岛洪堡冰川冰盖动力学进行建模，以及采用同一物理模型在两种不同分辨率下的应用。