MetaPINNs:Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization

Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.

Impact of intensity variability of the Asian summer monsoon anticyclone on the chemical distribution in the upper troposphere and lower stratosphere

亚洲夏季风期,平流层-对流层物质交换过程能显著影响上对流层下平流层化学成分的浓度变化和空间分布.然而,亚洲夏季风反气旋强度的季节内变化对其内部和周围地区化学成分水平分布的影响尚不清楚.本文将亚洲夏季风反气旋划分为季节内强周期和弱周期,发现当亚洲夏季风反气旋更强时,100 hPa O_(3)低值区的面积更大,O_(3)浓度更低.但是这种影响主要体现在6月份,7,8月的O_(3)水平分布还受东南亚地区深对流的影响.这些结果表明亚洲夏季风反气旋强度和深对流的季节内变化可以显著影响亚洲夏季风期上对流层下平流层的化学分布.

Solving nonlinear soliton equations using improved physics-informed neural networks with adaptive mechanisms

Partial differential equations(PDEs)are important tools for scientific research and are widely used in various fields.However,it is usually very difficult to obtain accurate analytical solutions of PDEs,and numerical methods to solve PDEs are often computationally intensive and very time-consuming.In recent years,Physics Informed Neural Networks(PINNs)have been successfully applied to find numerical solutions of PDEs and have shown great potential.All the while,solitary waves have been of great interest to researchers in the field of nonlinear science.In this paper,we perform numerical simulations of solitary wave solutions of several PDEs using improved PINNs.The improved PINNs not only incorporate constraints on the control equations to ensure the interpretability of the prediction results,which is important for physical field simulations,in addition,an adaptive activation function is introduced.By introducing hyperparameters in the activation function to change the slope of the activation function to avoid the disappearance of the gradient,computing time is saved thereby speeding up training.In this paper,the m Kd V equation,the improved Boussinesq equation,the Caudrey–Dodd–Gibbon–Sawada–Kotera equation and the p-g BKP equation are selected for study,and the errors of the simulation results are analyzed to assess the accuracy of the predicted solitary wave solution.The experimental results show that the improved PINNs are significantly better than the traditional PINNs with shorter training time but more accurate prediction results.The improved PINNs improve the training speed by more than 1.5 times compared with the traditional PINNs,while maintaining the prediction error less than 10~(-2)in this order of magnitude.

Assimilation of HY-2A scatterometer sea surface wind data in a 3DVAR data assimilation system-A case study of Typhoon Bolaven

The scatterometer （SCAT） on-board China＇s HY-2A satellite has the capability to provide high resolution wind vector information over the global ocean surface. These wind vector data produced by the HY-2A scatterometer （HY-2A SCAT） are available to the data assimilation system with real-time information of high accuracy. In this paper, two experiments are designed to investigate the impact of HY-2A SCAT data in the three- dimensional variational assimilation system for the Weather Research and Forecast model （WRF 3DVAR）. The powerful Typhoon Bolaven, which struck South Korea in August 2012, is selected for this case study. The results clearly demonstrate that HY-2A SCAT data can effectively complement the scarce observations over the ocean surface and improve the prediction of the wind and pressure fields of a typhoon. The case study of Typhoon Bolaven exhibits the significant and positive impact of HY- 2A SCAT data on the numerical prediction of the tropical cyclone track.

Assimilation of HY-2A Scatterometer Ambiguous Winds Based on Feature Thinning

This paper focuses on the data assimilation methods for sea surface winds, based on the level-2B HY-2A satellite microwave scatterometer wind products. We propose a new feature thinning method, which is herein used to screen scatterometer winds while maintaining the key structure of the wind field in the process of data thinning for highresolution satellite observations. We also accomplish feeding the ambiguous wind solutions directly into the data assimilation system, thus making better use of the retrieved information while simplifying the assimilation process of the scatterometer products. A numerical simulation experiment involving Typhoon Danas shows that our method gives better results than the traditional approach. This method may be a valuable alternative for operational satellite data assimilation.

Assimilation of All-Sky Radiance from the FY-3 MWHS-2 with the Yinhe 4D-Var System

Compared with traditional microwave humidity sounding capabilities at 183 GHz,new channels at 118 GHz have been mounted on the second generation of the Microwave Humidity Sounder(MWHS-2)onboard the Chinese FY-3C and FY-3D polar orbit meteorological satellites,which helps to perform moisture sounding.In this study,as the allsky approach can manage non-linear and non-Gaussian behavior in cloud-and precipitation-affected satellite radiances,the MWHS-2 radiances in all-sky conditions were first assimilated in the Yinhe four-dimensional variational data assimilation(YH4DVAR)system.The data quality from MWHS-2 was evaluated based on observation minus background statistics.It is found that the MWHS-2 data of both FY-3C and FY-3D are of good quality in general.Six months of MWHS-2 radiances in all-sky conditions were then assimilated in the YH4DVAR system.Based on the forecast scores and observation fits,we conclude that the all-sky assimilation of the MWHS-2 at 118-and 183-GHz channels on FY-3C/D is beneficial to the analysis and forecast fields of the temperature and humidity,and the impact on the forecast skill scores is neutral to positive.Additionally,we compared the impacts of assimilating the 118-GHz channels and the equivalent Advanced Microwave Sounding Unit-A(AMSUA)channels on global forecast accuracy in the absence of other satellite observations.Overall,the impact of the 118-GHz channels on the forecast accuracy is not as large as that for the equivalent AMSUA channels.Nevertheless,all-sky radiance assimilation of MWHS-2 in the YH4DVAR system has indeed benefited from the 118-GHz channels.