The various studies of partial differential equations (PDEs) are hot topics of mathematical research. Among them, solving PDEs is a very important and difficult task and, since many partial differential equations do not have analytical solutions, numerical methods are widely used to solve PDEs. Although numerical methods have been widely used with good performance, researchers are still searching for new methods for solving partial differential equations. In recent years, deep learning has achieved great success in many fields, such as image classification and natural language processing. Studies have shown that deep neural networks have powerful function-fitting capabilities and have great potential in the study of partial differential equations. In this paper, we introduce an improved Physics Informed Neural Network (PINN) for solving partial differential equations. PINN takes the physical information that is contained in partial differential equations as a regularization term, which improves the performance of neural networks. In this study, we use the method to study the wave equation, the KdV–Burgers equation, and the KdV equation. The experimental results show that PINN is effective in solving partial differential equations and deserves further research.

Cloud detection is an important and difficult task in the pre-processing of satellite remote sensing data. The results of traditional cloud detection methods are often unsatisfactory in complex environments or the presence of various noise disturbances. With the rapid development of artificial intelligence technology, deep learning methods have achieved great success in many fields such as image processing, speech recognition, autonomous driving, etc. This study proposes a deep learning model suitable for cloud detection, Cloud-AttU, which is based on a U-Net network and incorporates an attention mechanism. The Cloud-AttU model adopts the symmetric Encoder-Decoder structure, which achieves the fusion of high-level features and low-level features through the skip-connection operation, making the output results contain richer multi-scale information. This symmetrical network structure is concise and stable, significantly enhancing the effect of image segmentation. Based on the characteristics of cloud detection, the model is improved by introducing an attention mechanism that allows model to learn more effective features and distinguish between cloud and non-cloud pixels more accurately. The experimental results show that the method proposed in this paper has a significant accuracy advantage over the traditional cloud detection method. The proposed method is also able to achieve great results in the presence of snow/ice disturbance and other bright non-cloud objects, with strong resistance to disturbance. The Cloud-AttU model proposed in this study has achieved excellent results in the cloud detection tasks, indicating that this symmetric network architecture has great potential for application in satellite image processing and deserves further research.

El Niño is an important quasi-cyclical climate phenomenon that can have a significant impact on ecosystems and societies. Due to the chaotic nature of the atmosphere and ocean systems, traditional methods (such as statistical methods) are difficult to provide accurate El Niño index predictions. The latest research shows that Ensemble Empirical Mode Decomposition (EEMD) is suitable for analyzing non-linear and non-stationary signal sequences, Convolutional Neural Network (CNN) is good at local feature extraction, and Recurrent Neural Network (RNN) can capture the overall information of the sequence. As a special RNN, Long Short-Term Memory (LSTM) has significant advantages in processing and predicting long, complex time series. In this paper, to predict the El Niño index more accurately, we propose a new hybrid neural network model, EEMD-CNN-LSTM, which combines EEMD, CNN, and LSTM. In this hybrid model, the original El Niño index sequence is first decomposed into several Intrinsic Mode Functions (IMFs) using the EEMD method. Next, we filter the IMFs by setting a threshold, and we use the filtered IMFs to reconstruct the new El Niño data. The reconstructed time series then serves as input data for CNN and LSTM. The above data preprocessing method, which first decomposes the time series and then reconstructs the time series, uses the idea of symmetry. With this symmetric operation, we extract valid information about the time series and then make predictions based on the reconstructed time series. To evaluate the performance of the EEMD-CNN-LSTM model, the proposed model is compared with four methods including the traditional statistical model, machine learning model, and other deep neural network models. The experimental results show that the prediction results of EEMD-CNN-LSTM are not only more accurate but also more stable and reliable than the general neural network model.

Accumulating evidence has established that periodontitis was an independent risk factor for coronary heart disease (CAD). (), a major periodontal pathogen, has already been shown to have a significant role in the inflammatory response of CAD . The aim of the present study was to identify whether heat-shock protein 60 (HSP60) induced the dysfunction of human umbilical vein endothelial cells (HUVECs) . HUVECs were stimulated with a range of HSP60 concentrations (1, 10 and 100 ng/l) at different time-points. The levels of vascular endothelial (VE)-cadherin, endothelial nitric oxide synthase (eNOS) and cysteinyl aspartate-specific protease-3 (caspase-3) were measured using western blot analysis. The apoptotic rate of HUVECs was detected using flow cytometry. HSP60 at a concentration of 10 ng/l significantly decreased the expression levels of VE-cadherin and eNOS protein at 24 h stimulation, whereas no difference in these proteins was identified following a low dose of HSP60 (1 ng/l). HSP60 at 100 ng/l significantly downregulated the expression levels of VE-cadherin and eNOS protein at 12 h in HUVECs. However, the cleavage of caspase-3 showed an opposing change at different concentrations. Consistently, HSP60 induced apoptosis of HUVECs in a concentration-dependent manner. These results indicated that HSP60 may induce dysfunction and apoptosis in HUVECs via downregulating the expression levels of VE-cadherin and eNOS, and promoting the cleavage of caspase-3.

Chaotic systems are complex dynamical systems that play a very important role in the study of the atmosphere, aerospace engineering, finance, etc. To improve the accuracy of chaotic time series prediction, this study proposes a hybrid model CEEMDAN-LSTM which combines Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and long short-term memory (LSTM). In the model, the original time series is decomposed into several intrinsic mode functions (IMFs) and a residual component. To reduce the difficulty of predicting chaotic time series and provide a high level of predictive accuracy, the LSTM prediction model is built for all each characteristic series from CEEMDAN deposition. Finally, the final prediction results are obtained by combining all the prediction sequences. To test the effectiveness of this model we proposed, we examined the CEEMDAN-LSTM model using the Lorenz-63 system. Further compared to Autoregressive Integrated Moving Average (ARIMA ), Support Vector Regression (SVR), multilayer perceptron (MLP), and the single LSTM model, the results of the experiment show that the proposed model performs better in the prediction of chaotic time series. Besides, the hybrid model proposed in this paper has better results than the LSTM model alone. Therefore, hybrid models based on deep learning methods and signal decomposition methods have great potential in the field of chaotic time series prediction.

A new method for data assimilation is proposed using complex-variable differentiation (CVD), which can be used to estimate the initial conditions of the nonlinear physical system governed by the following equation:. Firstly, the gradient analysis of cost function in variational data assimilation is transformed into function numerical computation in complex domain, and the value of gradient is computed more efficiently and exactly. Secondly, the new algorithm of data assimilation is developed by combining an accurate gradient information from CVD with the classical optimization method. Finally, numerical simulations of typical chaotic systems and a humidity evolution equation with physical on-off process show that the new data assimilation method can reconstruct initial conditions of the nonlinear dynamical system very conveniently and accurately.

The variation of polar vortex intensity is a significant factor affecting the atmospheric conditions and weather in the Northern Hemisphere (NH) and even the world. However, previous studies on the prediction of polar vortex intensity are insufficient. This paper establishes a deep learning (DL) model for multi-day and long-time intensity prediction of the polar vortex. Focusing on the winter period with the strongest polar vortex intensity, geopotential height (GPH) data of NCEP from 1948 to 2020 at 50 hPa are used to construct the dataset of polar vortex anomaly distribution images and polar vortex intensity time series. Then, we propose a new convolution neural network with long short-term memory based on Gaussian smoothing (GSCNN-LSTM) model which can not only accurately predict the variation characteristics of polar vortex intensity from day to day, but also can produce a skillful forecast for lead times of up to 20 days. Moreover, the innovative GSCNN-LSTM model has better stability and skillful correlation prediction than the traditional and some advanced spatiotemporal sequence prediction models. The accuracy of the model suggests important implications that DL methods have good applicability in forecasting the nonlinear system and vortex spatial–temporal characteristics variation in the atmosphere.

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