提出I²PFL方法，同时利用域内和域间原型缓解联邦学习中的数据分布差异。

Federated Learning (FL) has emerged as a decentralized machine learning technique, allowing clients to train a global model collaboratively without sharing private data. However, most FL studies ignore the crucial challenge of heterogeneous domains where each client has a distinct feature distribution, which is popular in real-world scenarios. Prototype learning, which leverages the mean feature vectors within the same classes, has become a prominent solution for federated learning under domain shift. However, existing federated prototype learning methods focus soley on inter-domain prototypes and neglect intra-domain perspectives. In this work, we introduce a novel federated prototype learning method, namely I$^2$PFL, which incorporates $\textbf{I}$ntra-domain and $\textbf{I}$nter-domain $\textbf{P}$rototypes, to mitigate domain shift from both perspectives and learn a generalized global model across multiple domains in federated learning. To construct intra-domain prototypes, we propose feature alignment with MixUp-based augmented prototypes to capture the diversity within local domains and enhance the generalization of local features. Additionally, we introduce a reweighting mechanism for inter-domain prototypes to generate generalized prototypes that reduce domain shift while providing inter-domain knowledge across multiple clients. Extensive experiments on the Digits, Office-10, and PACS datasets illustrate the superior performance of our method compared to other baselines.