A Subgradient Method for Free Material Design

A small improvement in the structure of the material could save the manufactory a lot of money. The free material design can be formulated as an optimization problem. However, due to its large scale, second-order methods cannot solve the free material design problem in reasonable size. We formulate the free material optimization (FMO) problem into a saddle-point form in which the inverse of the stiffness matrix A(E) in the constraint is eliminated. The size of A(E) is generally large, denoted as N by N. This is the first formulation of FMO without A(E). We apply the primal-dual subgradient method [17] to solve the restricted saddle-point formula. This is the first gradient-type method for FMO. Each iteration of our algorithm takes a total of $O(N^2)$ foating-point operations and an auxiliary vector storage of size O(N), compared with formulations having the inverse of A(E) which requires $O(N^3)$ arithmetic operations and an auxiliary vector storage of size $O(N^2)$. To solve the problem, we developed a closed-form solution to a semidefinite least squares problem and an efficient parameter update scheme for the gradient method, which are included in the appendix. We also approximate a solution to the bounded Lagrangian dual problem. The problem is decomposed into small problems each only having an unknown of k by k (k = 3 or 6) matrix, and can be solved in parallel. The iteration bound of our algorithm is optimal for general subgradient scheme. Finally we present promising numerical results.Comment: SIAM Journal on Optimization (accepted

Bayesian optimization for materials design

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality

Optimisation of an ultrasonic drill horn for planetary subsurface sample retrieval

Ultrasonic tools can cut through foodstuffs, biological material and other soft matter with relative ease. However, when attempts are made to cut through harder material, the rate of progress markedly declines. Under such circumstances it is sometimes necessary to reduce the frequency of the blows delivered to the target, in order to ensure that each blow exceeds the compressive strength of the material, but for space applications the small size of high-frequency ultrasonic horns is extremely attractive. This paper therefore considers the optimization of horns for exploitation of the high-frequency/low-frequency drilling technique, whereby a free-mass oscillating between the horn and the target is employed to reduce the frequency at which impulse events are delivered to the target

Topological Insulators by Topology Optimization

An acoustic topological insulator (TI) is synthesized using topology optimization, a free material inverse design method. The TI appears spontaneously from the optimization process without imposing requirements on the existence of pseudo spin-1/2 states at the TI interface edge, or the Chern number of the topological phases. The resulting TI is passive; consisting of acoustically hard members placed in an air background and has an operational bandwidth of $\approx$12.5\% showing high transmission. Further analysis demonstrates confinement of more than 99\% of the total field intensity in the TI within at most six lattice constants from the TI interface. The proposed design hereby outperforms a reference from recent literature regarding energy transmission, field confinement and operational bandwidth.Comment: 6 pages, 5 figure

Scale-free Networks from Optimal Design

A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being one of them. In this letter we present the first evidence for the emergence of scaling (and smallworldness) in software architecture graphs from a well-defined local optimization process. Although the rules that define the strategies involved in software engineering should lead to a tree-like structure, the final net is scale-free, perhaps reflecting the presence of conflicting constraints unavoidable in a multidimensional optimization process. The consequences for other complex networks are outlined.Comment: 6 pages, 2 figures. Submitted to Europhysics Letters. Additional material is available at http://complex.upc.es/~sergi/software.ht

Electromagnetic Design of Dual Resonant Structures for Improved Sensitivity of Terahertz Label Free Bio-Sensing

A design is proposed exploiting full wave numerical simulation of a dual resonant structure with an aim to sense small amounts of chemical and biochemical materials. The structure is energized with free space radiation in the terahertz regime. Thanks to its asymmetric geometry two close resonances are excited. The interference between these two resonances produces a sharp change in the frequency response of the system. By selectively loading the structure with only small amounts of probe material, a relatively large shift in the frequency response may be achieved. The concept is demonstrated through simulation, while optimization of the structure and the analyte loading is attempted