The mathematical foundations of a new theory for the design of intelligent agents are presented. The proposed learning paradigm is centered around the concept of constraint, representing the interactions with the environment, and the parsimony principle. The classical regularization framework of kernel machines is naturally extended to the case in which the agents interact with a richer environment, where abstract granules of knowledge, compactly described by different linguistic formalisms, can be translated into the unified notion of constraint for defining the hypothesis set. Constrained variational calculus is exploited to derive general representation theorems that provide a description of the optimal body of the agent (i.e., the functional structure of the optimal solution to the learning problem), which is the basis for devising new learning algorithms. We show that regardless of the kind of constraints, the optimal body of the agent is a support constraint machine (SCM) based on representer theorems that extend classical results for kernel machines and provide new representations. In a sense, the expressiveness of constraints yields a semantic-based regularization theory, which strongly restricts the hypothesis set of classical regularization. Some guidelines to unify continuous and discrete computational mechanisms are given so as to accommodate in the same framework various kinds of stimuli, for example, supervised examples and logic predicates. The proposed view of learning from constraints incorporates classical learning from examples and extends naturally to the case in which the examples are subsets of the input space, which is related to learning propositional logic clauses.

No abstract

A parametric beam lattice model is formulated to analyse the propagation properties of

Recently, an increasing research effort has been dedicated to analyse the transmission and dispersion properties of periodic acoustic metamaterials, characterized by the presence of local resonators. Within this context, particular attention has been paid to the optimization of the amplitudes and center frequencies of selected stop and pass bands inside the Floquet-Bloch spectra of the acoustic metamaterials featured by a chiral or antichiral microstructure. Novel functional applications of such research are expected in the optimal parametric design of smart tunable mechanical filters and directional waveguides. The present paper deals with the maximization of the amplitude of low-frequency band gaps, by proposing suitable numerical techniques to solve the associated optimization problems. Specifically, the feasibility and effectiveness of Radial Basis Function networks and Quasi-Monte Carlo methods for the interpolation of the objective functions of such optimization problems are discussed, and their numerical application to a specific acoustic metamaterial with tetrachiral microstructure is presented. The discussion is motivated theoretically by the high computational effort often needed for an exact evaluation of the objective functions arising in band gap optimization problems, when iterative algorithms are used for their approximate solution. By replacing such functions with suitable surrogate objective functions constructed applying machine-learning techniques, well-performing suboptimal solutions can be obtained with a smaller computational effort. Numerical results demonstrate the effective potential of the proposed approach. Current directions of research involving the use of additional machine-learning techniques are also presented.

The elastic wave propagation is investigated in the beam lattice material characterized by a square periodic cell with anti-tetrachiral microstructure. With reference to the Floquet-Bloch spectrum, focus is made on the band structure enrichments and modifications which can be achieved by equipping the cellular microstructure with tunable local resonators. By virtue of its composite mechanical nature, the so-built inertial meta-material gains enhanced capacities of passive frequency-band filtering. Indeed the number, placement and properties of the inertial resonators can be designed to open, shift and enlarge the band gaps between one or more pairs of consecutive branches in the frequency spectrum. In order to improve the meta-material performance, a nonlinear optimization problem is formulated. The maximum of the largest band gap amplitudes in the low-frequency range is selected as suited objective function. Proper inequality constraints are introduced to restrict the optimal solutions within a compact set of mechanical and geometric parameters, including only physically realistic properties of both the lattice and resonators. The optimization problems related to full and partial band gaps are solved independently, by means of a globally convergent version of the numerical method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique.The optimal solutions are discussed and compared from the qualitative and quantitative viewpoints, bringing to light the limits and potential of the meta-material performance. The clearest trends emerging from the numerical analyses are pointed out and interpreted from the physical viewpoint. Finally, some specific recommendations about the microstructural design of the meta-material are synthesized.