We examine the deep learning technique referred to as the physics-informed neural network method for approximating the nonlinear Schr¨odinger equation under considered parity-time symmetric potentials and for obt...We examine the deep learning technique referred to as the physics-informed neural network method for approximating the nonlinear Schr¨odinger equation under considered parity-time symmetric potentials and for obtaining multifarious soliton solutions.Neural networks to found principally physical information are adopted to figure out the solution to the examined nonlinear partial differential equation and to generate six different types of soliton solutions,which are basic,dipole,tripole,quadruple,pentapole,and sextupole solitons we consider.We make comparisons between the predicted and actual soliton solutions to see whether deep learning is capable of seeking the solution to the partial differential equation described before.We may assess whether physicsinformed neural network is capable of effectively providing approximate soliton solutions through the evaluation of squared error between the predicted and numerical results.Moreover,we scrutinize how different activation mechanisms and network architectures impact the capability of selected deep learning technique works.Through the findings we can prove that the neural networks model we established can be utilized to accurately and effectively approximate the nonlinear Schr¨odinger equation under consideration and to predict the dynamics of soliton solution.展开更多
首次报道非主要农作物新品种‘奇雅1号’在湖南省5个不同试种点的种植表现及主要栽培管理技术,并对其农艺性状进行连续2年的观测记录,重点分析与产量相关的性状。结果表明：奇雅1号适应亚热带季风性湿润气候,生长期在200 d左右,是典型...首次报道非主要农作物新品种‘奇雅1号’在湖南省5个不同试种点的种植表现及主要栽培管理技术,并对其农艺性状进行连续2年的观测记录,重点分析与产量相关的性状。结果表明：奇雅1号适应亚热带季风性湿润气候,生长期在200 d左右,是典型的短日照植物;播种时间为4月下旬或5月上旬;发芽的最适气温为25℃;播种基质为p H 6.5~7.0的沙壤或粘土;收获时间为11月下旬;通过主成分分析,在众多的农艺性状中,与产量高度相关的是分枝数和花序数。展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12075034)。
文摘We examine the deep learning technique referred to as the physics-informed neural network method for approximating the nonlinear Schr¨odinger equation under considered parity-time symmetric potentials and for obtaining multifarious soliton solutions.Neural networks to found principally physical information are adopted to figure out the solution to the examined nonlinear partial differential equation and to generate six different types of soliton solutions,which are basic,dipole,tripole,quadruple,pentapole,and sextupole solitons we consider.We make comparisons between the predicted and actual soliton solutions to see whether deep learning is capable of seeking the solution to the partial differential equation described before.We may assess whether physicsinformed neural network is capable of effectively providing approximate soliton solutions through the evaluation of squared error between the predicted and numerical results.Moreover,we scrutinize how different activation mechanisms and network architectures impact the capability of selected deep learning technique works.Through the findings we can prove that the neural networks model we established can be utilized to accurately and effectively approximate the nonlinear Schr¨odinger equation under consideration and to predict the dynamics of soliton solution.
文摘首次报道非主要农作物新品种‘奇雅1号’在湖南省5个不同试种点的种植表现及主要栽培管理技术,并对其农艺性状进行连续2年的观测记录,重点分析与产量相关的性状。结果表明：奇雅1号适应亚热带季风性湿润气候,生长期在200 d左右,是典型的短日照植物;播种时间为4月下旬或5月上旬;发芽的最适气温为25℃;播种基质为p H 6.5~7.0的沙壤或粘土;收获时间为11月下旬;通过主成分分析,在众多的农艺性状中,与产量高度相关的是分枝数和花序数。
