Neural Optimization Machine for Analytical Function Optimization: Application to Auxetic Metamaterial Design

In this study, a novel neural network-based optimization framework, called as Neural Optimization Machine (NOM) is presented toaddress constrained, unconstrained, and multi-objective optimization problems to design optimal auxetic metamaterial structures.Unlike conventional gradient-based and other traditional evolutionary solvers, the NOM constructs a surrogate model of theobjective function and integrates it into a neural architecture. NOM embeds the trained neural surrogate as the objective function,achieving end-to-end differentiable optimization. This yields high accuracy with reduced computation time (up to 20-25% fasterthan Genetic Algorithm). NOM’s performance is tested comprehensively on test functions (such as McCormick, Rosenbrock,and Mishra’s Bird). The framework is validated with computational experiments through optimization of a re-entrant auxeticmetamaterial structure design, achieving an optimal negative Poisson’s Ratio, ν = -1.55, showcasing NOM’s direct applicability toengineering structures, viz. a monolithic smart morphing wing. The results highlight NOM’s versatility and scalability, paving theway for broader applications in topology optimization, aerodynamic design, and material science.