EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction With Exogenous Variables.

While exogenous variables have a major impact on performance improvement in time series analysis, interseries correlation and time dependence among them are rarely considered in the present continuous methods. The dynamical systems of multivariate time series could be modeled with complex unknown partial differential equations (PDEs) which play a prominent role in many disciplines of science and engineering. In this article, we propose a continuous-time model for arbitrary-step prediction to learn an unknown PDE system in multivariate time series whose governing equations are parameterized by self-attention and gated recurrent neural networks. The proposed model, exogenous-guided PDE network (EgPDE-Net), takes account of the relationships among the exogenous variables and their effects on the target series. Importantly, the model can be reduced into a regularized ordinary differential equation (ODE) problem with specially designed regularization guidance, which makes the PDE problem tractable to obtain numerical solutions and feasible to predict multiple future values of the target series at arbitrary time points. Extensive experiments demonstrate that our proposed model could achieve competitive accuracy over strong baselines: on average, it outperforms the best baseline by reducing 9.85% on RMSE and 13.98% on MAE for arbitrary-step prediction.

Generalized image outpainting with U-transformer.

In this paper, we develop a novel transformer-based generative adversarial neural network called U-Transformer for generalized image outpainting problems. Different from most present image outpainting methods conducting horizontal extrapolation, our generalized image outpainting could extrapolate visual context all-side around a given image with plausible structure and details even for complicated scenery, building, and art images. Specifically, we design a generator as an encoder-to-decoder structure embedded with the popular Swin Transformer blocks. As such, our novel neural network can better cope with image long-range dependencies which are crucially important for generalized image outpainting. We propose additionally a U-shaped structure and multi-view Temporal Spatial Predictor (TSP) module to reinforce image self-reconstruction as well as unknown-part prediction smoothly and realistically. By adjusting the predicting step in the TSP module in the testing stage, we can generate arbitrary outpainting size given the input sub-image. We experimentally demonstrate that our proposed method could produce visually appealing results for generalized image outpainting against the state-of-the-art image outpainting approaches.