Y. Nie

Z. Yang, Z. Yuan, Y. Nie et al.

In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.

L. Xiao, J. Xu, D. Zhao et al.

We consider the problem of unsupervised domain adaptation for image classification. To learn target-domain-aware features from the unlabeled data, we create a self-supervised pretext task by augmenting the unlabeled data with a certain type of transformation (specifically, image rotation) and ask the learner to predict the properties of the transformation. However, the obtained feature representation may contain a large amount of irrelevant information with respect to the main task. To provide further guidance, we force the feature representation of the augmented data to be consistent with that of the original data. Intuitively, the consistency introduces additional constraints to representation learning, therefore, the learned representation is more likely to focus on the right information about the main task. Our experimental results validate the proposed method and demonstrate state-of-the-art performance on classical domain adaptation benchmarks. Code is available at https://github.com/Jiaolong/ss-da-consistency.