Computational design of innovative mechanical metafilters via adaptive surrogate-based optimization

On principal component analysis of the convex combination of two data matrices and its application to acoustic metamaterial filters

“…We conclude mentioning that, in our related work [5] about the design of acoustic metamaterial filters according to a single-objective optimization framework 3 (see [1] for a physical-mathematical model similar to the one considered in [5]), we have successfully applied PCA to the sampled gradient field of the objective function, achieving numerical results comparable with those obtained by using the exact gradient, but with a much smaller computational effort (e.g., with a reduction of the dimension by a factor 4). A similar outcome is expected 1 It is common practice to apply PCA to centered (also called de-meaned) data matrices X (c) , i.e., having the form X (c) .…”

“…For rigorous definitions, see [11,12] and the references therein. 3 Such optimization problems are typically characterized by a high computational effort needed for an exact evaluation of the gradient of their objective functions, which is motivated by the fact that each such evaluation requires solving the physicalmathematical model associated with the specific choice of the vector of parameters of the model, which is also the vector of optimization variables. The reader is referred to [2] for a further discussion about these computational issues.…”

Convex combination of data matrices: PCA perturbation bounds for multi-objective optimal design of mechanical metafilters

“…This is the subject of investigation of our ongoing work [3]. So, for the case of the multi-objective optimal design of mechanical metamaterial filters, the application of PCA to the approximation of the sampled gradient field of a suitable associated single-objective function (which represents a proper trade-off between two or more different objectives) can be a valid alternative to the use of surrogate optimization methods (which replace the original objective function with a surrogate function, learned either offline [4] or online [2]), in case a gradient-based optimization algorithm is used to solve the optimization problem. It is also worth mentioning that this particular application of PCA to the multi-objective optimal design of mechanical metamaterial filters, combined with a multi-start optimization approach, has been the source of inspiration for the theoretical investigation made in the present article.…”

“…The application of the theoretical analysis to multi-objective optimization is discussed extensively in the article, together with possible extensions of such theoretical analysis. In more details, the cases of unconstrained multi-objective maximization with quadratic and concave objective functions [1] and of the multi-objective optimal design of metamaterial filters [19,2] are investigated.…”

An Improved Tandem Neural Network Architecture for Inverse Modeling of Multicomponent Reactive Transport in Porous Media

“…That is to say, the inverse modeling results of TNNA are determined by the approximate accuracy of forward network in this small area. Thus, the adaptive updating strategy (AUS) is introduced to force the surrogate model to be locally accurate in the region around true parameter values (Bacigalupo et al, 2021;C. Wang et al, 2014;G.…”