In recent years, considerable research advancements have emerged in the application of inverse design methods to enhance the performance of electromagnetic (EM) metamaterials. Notably, the integration of deep learning (DL) technologies, with their robust capabilities in data analysis, categorization, and interpretation, has demonstrated revolutionary potential in optimization algorithms for improved efficiency. In this review, current inverse design methods for EM metamaterials are presented, including topology optimization (TO), evolutionary algorithms (EAs), and DL-based methods. Their application scopes, advantages and limitations, as well as the latest research developments are respectively discussed. The classical iterative inverse design methods categorized TO and EAs are discussed separately, for their fundamental role in solving inverse design problems. Also, attention is given on categories of DL-based inverse design methods, i.e. classifying into DL-assisted, direct DL, and physics-informed neural network methods. A variety of neural network architectures together accompanied by relevant application examples are highlighted, as well as the practical utility of these overviewed methods. Finally, this review provides perspectives on potential future research directions of EM metamaterials inverse design and integrated artificial intelligence methodologies.

This study focused on the dynamical behavior analysis of a discrete fractional Leslie-Gower model incorporating antipredator behavior and a Holling type Ⅱ functional response. Initially, we analyzed the existence and stability of the model's positive equilibrium points. For the interior positive equilibrium points, we investigated the parameter conditions leading to period-doubling bifurcation and Neimark-Sacker bifurcation using the center manifold theorem and bifurcation theory. To effectively control the chaos resulting from these bifurcations, we proposed two chaos control strategies. Numerical simulations were conducted to validate the theoretical results. These findings may contribute to the improved management and preservation of ecological systems.

This paper investigates the dynamical behavior of a discrete fractional-order modified Leslie–Gower model with a Michaelis–Menten-type harvesting mechanism and a Holling-II functional response. We analyze the existence and stability of the nonnegative equilibrium points. For the interior equilibrium points, we study the conditions for period-doubling and Neimark–Sacker bifurcations using the center manifold theorem and bifurcation theory. To control the chaos arising from these bifurcations, two chaos control strategies are proposed. Numerical simulations are performed to validate the theoretical results. The findings provide valuable insights into the sustainable management and conservation of ecological systems.

This paper introduces a highly accurate and efficient conservative scheme for solving the nonlocal damped Schrödinger system with Riesz fractional derivatives. The proposed approach combines the Fourier spectral method with the Crank–Nicolson time-stepping scheme. To begin, the original equation is reformulated into an equivalent system by introducing a new variable that modifies both energy and mass. The Fourier spectral method is employed to achieve high spatial accuracy in this semi-discrete formulation. For time discretization, the Crank–Nicolson scheme is applied, ensuring conservation of the modified energy and mass in the fully discrete system. Numerical experiments validate the scheme’s precision and its ability to preserve conservation properties.