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This paper presents a novel approach for solving the shallow-water transport equation using a physics-informed neural network (PINN) combined with characteristic-based split (CBS). Simulation of the tide in East Coast of China is performed to verify the applicability of the present method in a practical problem. Furthermore, we propose a boundary condition that accounts for the second-order partial derivative term, which is more appropriate for solving the diffusion equation with open domains than the commonly used assumption of zero boundary values. Our numerical results demonstrate that this boundary condition leads to improved convergence of the network. In addition, we introduce a parameter estimation method that requires information from the field at only two different times, yet yields accurate parameter estimates. We observe that excessive participation of variables in gradient backpropagation can lead to neural networks getting trapped in local optima. We use PINN combined with CBS method to solve 3-D incompressible flow. As the number of variables involved in gradient backpropagation increases, the accuracy of the solution decreases, which can partially support our viewpoint. The source codes for the numerical examples in this work are available at https://github.com/double110/PINN-cbs-.git. • We introduce a rapid version of PINN and solve 3-d incompressible flow. • We introduce a boundary condition in open domains to enhance accuracy and stability. • We develop a PINN-CBS method for parameter estimation. • Reduce the number of variables participating in backpropagation can improve accuracy. [ABSTRACT FROM AUTHOR]

Predicting stock market trends is the basic daily routine task that investors should perform in the stock trading market. Traditional market trends prediction models are generally based on hand-crafted factors or features, which heavily rely on expensive expertise knowledge. Moreover, it is difficult to discover hidden features contained in the stock time series data, which are otherwise helpful for predicting stock market trends. In this paper, we propose a novel stock market trends prediction framework SMART with a self-supervised stock technical data sequence embedding model S3E. Specifically, the model encodes stock technical data sequences into embeddings, which are further trained with multiple self-supervised auxiliary tasks. With the learned sequence embeddings, we make stock market trends predictions based on an LSTM and a feed-forward neural network. We conduct extensive experiments on China A-Shares market and NASDAQ market to show that our model is highly effective for stock market trends prediction. We further deploy SMART in a leading financial service provider in China and the result demonstrates the effectiveness of the proposed method in real-world applications. [ABSTRACT FROM AUTHOR]