Exploring the potentialities of artificial neural networks on metamaterials topological design

Abstract

Artificial neural networks methods have been applied to solve many complex problems, in which analytical solutions are unknown and numerical approximations are very expensive to compute. Those methods are still underexplored on the field of topology optimization, where there is a great number of variables (from hundreds of thousands to millions), complex objective functions (which depends on inverses of high order matrices) and a series of intricate constraints (such as to avoid checkerboards and to take into account manufacturing limitations). Even for simpler cases, in usual methods, a large linear system must be solved for each topology update. The most precise and robust methods demand many iterations (hundreds at least) to obtain a solution and some heuristic methods, that demand less iterations, can be inaccurate and may even fail to provide a result (when the system's matrix becomes singular throughout the evolutionary process). Therefore, it is proposed to explore ways of speeding up the topology optimization of structures using neural networks, the following techniques will be developed, implemented and tested: to reduce the dimension of the problems by identifying minimal sets of features that can sufficiently define the topologies; to directly obtain near optimal topologies, from where the usual methods could be used to conclude the optimization in few iterations; to predict which would be the best variables' update for a known state (described by the problem settings and the current topology), it can be done by estimating the linear system response and then using a standard gradient-based method, or by directly assigning topology update actions. Each of these applications will be evaluated for the minimization of mean compliance or maximal stress on static structures, composed of homogeneous, isotropic, elastic material, under linear assumptions. This first exploration will allow a better understanding of the potential of neural networks on this field. After discarding any improper methods and refining the promising ones, they will be applied on the design of metamaterials. Those are materials projected to have desired properties, such as negative Poisson ratios, high thermal expansion coefficients and large band gaps. General multiphysics and multiscale problems will be approached primarily, since they are essential to the metamaterials topological design. (AU)