Efficient Elastic Net Regularization for Sparse Linear Models

This paper presents an algorithm for efficient training of sparse linear models with elastic net regularization. Extending previous work on delayed updates, the new algorithm applies stochastic gradient updates to non-zero features only, bringing weights current as needed with closed-form updates. Closed-form delayed updates for the $\ell_1$, $\ell_{\infty}$, and rarely used $\ell_2$ regularizers have been described previously. This paper provides closed-form updates for the popular squared norm $\ell^2_2$ and elastic net regularizers. We provide dynamic programming algorithms that perform each delayed update in constant time. The new $\ell^2_2$ and elastic net methods handle both fixed and varying learning rates, and both standard {stochastic gradient descent} (SGD) and {forward backward splitting (FoBoS)}. Experimental results show that on a bag-of-words dataset with $260,941$ features, but only $88$ nonzero features on average per training example, the dynamic programming method trains a logistic regression classifier with elastic net regularization over $2000$ times faster than otherwise

Object oriented design of a thermo-mechanical FEM code

An object oriented design is presented for a computer program that can perform\ud thermo-mechanically coupled analyzes. The target of the design is a \ud exible and robust\ud computer program. It should be easy to adapt and extend, re-using existing code, without\ud interfering with already established algorithms.\ud The program uses publicly available toolkits that are currently emerging as C++ pack-\ud ages. First of all the Standard C++ Library (formerly Standard Template Library) is\ud used for packing items in container classes. Secondly the matrix and vector operations\ud are derived from the Template Numerical Toolkit (TNT) and �nally (not essentially for\ud the numerical part) a graphical user interface is made, based on the wxWindows package,\ud that can generate a GUI for Motif and MS-Windows with the same code.\ud Attention is given to the design of classes such as speci�c elements and material classes\ud based on more general classes. A hierarchy of classes is constructed where general behavior\ud is put high in the hierarchy and speci�c behavior low. The choice between inheritance and\ud aggregation is made at several levels

PyFrac: A planar 3D hydraulic fracture simulator

Fluid driven fractures propagate in the upper earth crust either naturally or in response to engineered fluid injections. The quantitative prediction of their evolution is critical in order to better understand their dynamics as well as to optimize their creation. We present a Python implementation of an open-source hydraulic fracture propagation simulator based on the implicit level set algorithm originally developed by Peirce & Detournay (2008) -- "An implicit level set method for modeling hydraulically driven fractures". Comp. Meth. Appl. Mech. Engng, (33-40):2858--2885. This algorithm couples a finite discretization of the fracture with the use of the near tip asymptotic solutions of a steadily propagating semi-infinite hydraulic fracture. This allows to resolve the multi-scale processes governing hydraulic fracture growth accurately, even with relatively coarse meshes. We present an overview of the mathematical formulation, the numerical scheme and the details of our implementation. A series of problems including a radial hydraulic fracture verification benchmark, the propagation of a height contained hydraulic fracture, the lateral spreading of a magmatic dyke and the handling of fracture closure are presented to demonstrate the capabilities, accuracy and robustness of the implemented algorithm

InterCloud: Utility-Oriented Federation of Cloud Computing Environments for Scaling of Application Services

Cloud computing providers have setup several data centers at different geographical locations over the Internet in order to optimally serve needs of their customers around the world. However, existing systems do not support mechanisms and policies for dynamically coordinating load distribution among different Cloud-based data centers in order to determine optimal location for hosting application services to achieve reasonable QoS levels. Further, the Cloud computing providers are unable to predict geographic distribution of users consuming their services, hence the load coordination must happen automatically, and distribution of services must change in response to changes in the load. To counter this problem, we advocate creation of federated Cloud computing environment (InterCloud) that facilitates just-in-time, opportunistic, and scalable provisioning of application services, consistently achieving QoS targets under variable workload, resource and network conditions. The overall goal is to create a computing environment that supports dynamic expansion or contraction of capabilities (VMs, services, storage, and database) for handling sudden variations in service demands. This paper presents vision, challenges, and architectural elements of InterCloud for utility-oriented federation of Cloud computing environments. The proposed InterCloud environment supports scaling of applications across multiple vendor clouds. We have validated our approach by conducting a set of rigorous performance evaluation study using the CloudSim toolkit. The results demonstrate that federated Cloud computing model has immense potential as it offers significant performance gains as regards to response time and cost saving under dynamic workload scenarios.Comment: 20 pages, 4 figures, 3 tables, conference pape