A neural network(NN) is a powerful tool for approximating bounded continuous functions in machine learning. The NN provides a framework for numerically solving ordinary differential equations(ODEs) and partial differe...A neural network(NN) is a powerful tool for approximating bounded continuous functions in machine learning. The NN provides a framework for numerically solving ordinary differential equations(ODEs) and partial differential equations(PDEs)combined with the automatic differentiation(AD) technique. In this work, we explore the use of NN for the function approximation and propose a universal solver for ODEs and PDEs. The solver is tested for initial value problems and boundary value problems of ODEs, and the results exhibit high accuracy for not only the unknown functions but also their derivatives. The same strategy can be used to construct a PDE solver based on collocation points instead of a mesh, which is tested with the Burgers equation and the heat equation(i.e., the Laplace equation).展开更多
This paper presents a method of determining the friction coefficient in metal forming using multilayer artificial neural networks based on experimental data obtained from strip drawing test. The number of input variab...This paper presents a method of determining the friction coefficient in metal forming using multilayer artificial neural networks based on experimental data obtained from strip drawing test. The number of input variables of the artificial neural network has been optimized using genetic algorithm. This process is based on surface parameters of the sheet and dies, sheet material parameters and clamping force as input parameters to train the neural network. In addition to demonstrating the fact that regression statistics model using genetic selection and intelligent problem solver are better than models without preprocessing of input data, the sensitivity analysis of the input variables has been conducted. This avoids the time-consuming testing of neurons in finding the best network architecture. The obtained results from this study have also pointed out that genetic algorithm can successfully be applied to optimize the training set and the outputs agree with experimental results. This allows reduction or elimination of expensive experimental tests to determine friction coefficient value.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11521091)
文摘A neural network(NN) is a powerful tool for approximating bounded continuous functions in machine learning. The NN provides a framework for numerically solving ordinary differential equations(ODEs) and partial differential equations(PDEs)combined with the automatic differentiation(AD) technique. In this work, we explore the use of NN for the function approximation and propose a universal solver for ODEs and PDEs. The solver is tested for initial value problems and boundary value problems of ODEs, and the results exhibit high accuracy for not only the unknown functions but also their derivatives. The same strategy can be used to construct a PDE solver based on collocation points instead of a mesh, which is tested with the Burgers equation and the heat equation(i.e., the Laplace equation).
文摘This paper presents a method of determining the friction coefficient in metal forming using multilayer artificial neural networks based on experimental data obtained from strip drawing test. The number of input variables of the artificial neural network has been optimized using genetic algorithm. This process is based on surface parameters of the sheet and dies, sheet material parameters and clamping force as input parameters to train the neural network. In addition to demonstrating the fact that regression statistics model using genetic selection and intelligent problem solver are better than models without preprocessing of input data, the sensitivity analysis of the input variables has been conducted. This avoids the time-consuming testing of neurons in finding the best network architecture. The obtained results from this study have also pointed out that genetic algorithm can successfully be applied to optimize the training set and the outputs agree with experimental results. This allows reduction or elimination of expensive experimental tests to determine friction coefficient value.
基金the National Key Research and Development Program of China(973 Program)(No.2016YFA0301700)the Anhui Initiative in Quantum Information Technologies(No.AHY080000).
