GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs

With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs can efficiently handle high-dimensional problems, but the accuracy is relatively low, especially for highly irregular problems. Inspired by the idea of adaptive finite element methods and incremental learning, we propose GAS, a Gaussian mixture distribution-based adaptive sampling method for PINNs. During the training procedure, GAS uses the current residual information to generate a Gaussian mixture distribution for the sampling of additional points, which are then trained together with historical data to speed up the convergence of the loss and achieve higher accuracy. Several numerical simulations on 2D and 10D problems show that GAS is a promising method that achieves state-of-the-art accuracy among deep solvers, while being comparable with traditional numerical solvers.

Privacy-Preserved Blockchain-Federated-Learning for Medical Image Analysis Towards Multiple Parties

To share the patient\textquoteright s data in the blockchain network can help to learn the accurate deep learning model for the better prediction of COVID-19 patients. However, privacy (e.g., data leakage) and security (e.g., reliability or trust of data) concerns are the main challenging task for the health care centers. To solve this challenging task, this article designs a privacy-preserving framework based on federated learning and blockchain. In the first step, we train the local model by using the capsule network for the segmentation and classification of the COVID-19 images. The segmentation aims to extract nodules and classification to train the model. In the second step, we secure the local model through the homomorphic encryption scheme. The designed scheme encrypts and decrypts the gradients for federated learning. Moreover, for the decentralization of the model, we design a blockchain-based federated learning algorithm that can aggregate the gradients and update the local model. In this way, the proposed encryption scheme achieves the data provider privacy, and blockchain guarantees the reliability of the shared data. The experiment results demonstrate the performance of the proposed scheme.