The generalized continuous analog of Newton’s method for the numerical study of some nonlinear quantum-field models
A numerical method for studying nonlinear problems arising in mathematical models of physics is systematically described in this review. The unified basis for the development of numerical schemes is a generalization of the continuous analog of Newton’s method, which represents a qualitatively new development of the Newtonian evolution process on the basis of the integration of concepts from perturbation theory and the theory of evolution in parameters. The results are presented of numerical studies of quantum-field models of the polaron, the solvated electron, the binucleon, and also QCD potential models for some commonly used potentials.
Recent work has shown success in using neural network as ranking model in question answering(QA). While the precision of these models has increased significantly over time, most models need long training time, which leads to it cannot be used effectively in practical applications. In this paper, we propose a simple model to accelerate training speed with noise-contrastive estimation. This model mainly inspired by an architecture based entirely on convolutional neural networks and noise-contrastive estimation. We investigate the behavior of the model on the financial dataset which we use in practice and show that it reduces the training times by more than an order of magnitude without affecting the quality of the resulting models. The model is also more efficient and more stable than importance sampling because it requires fewer noise samples to perform well.