Optimization Design for the Electron Emission System Using Improved Powell Method

The electron emission system, which may mostly decide the main properties of the whole electron optical system, is a crucial element for an electron gun. The design of the electron emission system is more important compared with other electron lenses in the electron gun. In this paper, an optimization design method for the electron emission system is presented by using an Improved Powell Method with linear search for the one dimensional search. The optimal structure parameters with a criterion of minimum objective function value for this system are provided. The computed results may show that this direct search optimization method is feasible and useful for the optimal design of the electron emission system as well as other electron optical systems

Generative Adversarial Method Based on Neural Tangent Kernels

The recent development of Generative adversarial networks (GANs) has driven many computer vision applications. Despite the great synthesis quality, training GANs often confronts several issues, including non-convergence, mode collapse, and gradient vanishing. There exist several workarounds, for example, regularizing Lipschitz continuity and adopting Wasserstein distance. Although these methods can partially solve the problems, we argue that the problems are result from modeling the discriminator with deep neural networks. In this paper, we base on newly derived deep neural network theories called Neural Tangent Kernel (NTK) and propose a new generative algorithm called generative adversarial NTK (GA-NTK). The GA-NTK models the discriminator as a Gaussian Process (GP). With the help of the NTK theories, the training dynamics of GA-NTK can be described with a closed-form formula. To synthesize data with the closed-form formula, the objectives can be simplified into a single-level adversarial optimization problem. We conduct extensive experiments on real-world datasets, and the results show that GA-NTK can generate images comparable to those by GANs but is much easier to train under various conditions. We also study the current limitations of GA-NTK and propose some workarounds to make GA-NTK more practical