BPGrad: Towards Global Optimality in Deep Learning via Branch and Pruning

Understanding the global optimality in deep learning (DL) has been attracting more and more attention recently. Conventional DL solvers, however, have not been developed intentionally to seek for such global optimality. In this paper we propose a novel approximation algorithm, BPGrad, towards optimizing deep models globally via branch and pruning. Our BPGrad algorithm is based on the assumption of Lipschitz continuity in DL, and as a result it can adaptively determine the step size for current gradient given the history of previous updates, wherein theoretically no smaller steps can achieve the global optimality. We prove that, by repeating such branch-and-pruning procedure, we can locate the global optimality within finite iterations. Empirically an efficient solver based on BPGrad for DL is proposed as well, and it outperforms conventional DL solvers such as Adagrad, Adadelta, RMSProp, and Adam in the tasks of object recognition, detection, and segmentation

Simulation of hyperelastic materials in real-time using Deep Learning

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition, parallel computing, adaptive meshing, and model order reduction. In this paper we present U-Mesh: a data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm. We show that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly non-linear models in a compact form. Our method is applied to two benchmark examples: a cantilever beam and an L-shape subject to moving punctual loads. A comparison between our method and proper orthogonal decomposition (POD) is done through the paper. The results show that U-Mesh can perform very fast simulations on various geometries, mesh resolutions and number of input forces with very small errors

Rigidity and flexibility of biological networks

The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of protein structures, as well as local flexibility measures of proteins and their applications in explaining allostery and thermostability is given. We also briefly discuss the network aspects of cytoskeletal tensegrity. Finally, we show the importance of the balance between functional flexibility and rigidity in protein-protein interaction, metabolic, gene regulatory and neuronal networks. Our summary raises the possibility that the concepts of flexibility and rigidity can be generalized to all networks.Comment: 21 pages, 4 figures, 1 tabl

THE USE OF NEURAL NETWORKS IN THE SPATIAL ANALYSIS OF PROPERTY VALUES

The real-estate market is "where" a multiplicity of economic, cultural, social and demographic factors are synthesised with respect to choices regarding the qualitative and locational aspects of a property. The spatial analysis of the real-estate market and, in particular, of the factors which contribute to determining prices, is a very useful instrument in outlining the geography of the economic development of vast areas. The aim of the paper is the construction of a simulation model, on a spatial level, of real-estate values with reference to the housing market in the urban area of the city of Treviso (I). The model was built using a neural network which gives the possibility of analysing the marginal contribution of single real-estate characteristics independently of the a priori choice of the interpolation function; at the same time it works well even in the presence of statistical correlation among the explicative variables, a serious drawback in multiple regression models. The work is divided into several parts. First, a synthetic picture of the real-estate market of the area studied has been drawn up with reference to the main conditioning factors. Then the problem of the selection of a neural network model for the appraisal of property values is presented. Finally, there is the description of the procedure for the spatialization of obtained results from the neural model for the definition of a values map. The results shows the notable interpretative and predictive capacity of the neural model and it seems very useful in appraisals. Furthermore, the mapping of value fluctuations enables first-hand verification of the "goodness" of the assessed model and its capacity to portray the real situation. The general approach presented seems, therefore, useful both as an instrument of support for urban and territorial planning, as well as a permanent monitoring system of the real-estate market with the aim of creating an informative system of support for the analysis of real-estate investment.Land Economics/Use,