Meaningful finite element discretization scheme: a case for circular disk subjected to four radial loads

In finite element (FE) modelling, apart from proper element selection, selection of an appropriate discretization scheme is crucial in correctly evaluating the intended variables. Photoelasticity plays an effective role in selecting an appropriate discretization scheme for modelling problems in stress analysis. A meaningful FE discretization is very important in evaluating the desired parameters in FE analysis. The adaptive mesh refinement emphasizes the need for a meaningful discretization of domain. This paper presents a discretization strategy for meaningful discretization of the circular disk subjected to four equal radial loads. The work evolved the generation of software for the disk subjected to four radial loads perpendicular to each other. Due to symmetry of the problem only quarter of the disk is discretized

Greedy PIG: Adaptive Integrated Gradients

Deep learning has become the standard approach for most machine learning tasks. While its impact is undeniable, interpreting the predictions of deep learning models from a human perspective remains a challenge. In contrast to model training, model interpretability is harder to quantify and pose as an explicit optimization problem. Inspired by the AUC softmax information curve (AUC SIC) metric for evaluating feature attribution methods, we propose a unified discrete optimization framework for feature attribution and feature selection based on subset selection. This leads to a natural adaptive generalization of the path integrated gradients (PIG) method for feature attribution, which we call Greedy PIG. We demonstrate the success of Greedy PIG on a wide variety of tasks, including image feature attribution, graph compression/explanation, and post-hoc feature selection on tabular data. Our results show that introducing adaptivity is a powerful and versatile method for making attribution methods more powerful

An Exploration-exploitation Compromise-based Adaptive Operator Selection for Local Search

This paper deals with the adaptive selection of operators in the context of local search (LS). In evolutionary algorithms, diversity is a key concept. We consider a related idea: the similarity between the candidate solution and the solutions in the search trajectory. This notion, together with the solution quality, is used to evaluate the performance of each operator. A new utility measure for LS operators, evaluating relative distances between the operators, is introduced. It is compared with an existing measure based on the Pareto dominance relationship using some basic selection schemes. An adaptive version of the algorithm is also examined. The proposed methods are tested on the Quadratic Assignment Problem and Asymmetric Traveling Salesman Problem

Embedding Feature Selection for Large-scale Hierarchical Classification

Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select the subset of discriminant features is an effective strategy to deal with large-scale HC problem. It speeds up the training process, reduces the prediction time and minimizes the memory requirements by compressing the total size of learned model weight vectors. Majority of the studies have also shown feature selection to be competent and successful in improving the classification accuracy by removing irrelevant features. In this work, we investigate various filter-based feature selection methods for dimensionality reduction to solve the large-scale HC problem. Our experimental evaluation on text and image datasets with varying distribution of features, classes and instances shows upto 3x order of speed-up on massive datasets and upto 45% less memory requirements for storing the weight vectors of learned model without any significant loss (improvement for some datasets) in the classification accuracy. Source Code: https://cs.gmu.edu/~mlbio/featureselection.Comment: IEEE International Conference on Big Data (IEEE BigData 2016

Layered evaluation of interactive adaptive systems : framework and formative methods

Peer reviewedPostprin

Adaptive quadrature by expansion for layer potential evaluation in two dimensions

When solving partial differential equations using boundary integral equation methods, accurate evaluation of singular and nearly singular integrals in layer potentials is crucial. A recent scheme for this is quadrature by expansion (QBX), which solves the problem by locally approximating the potential using a local expansion centered at some distance from the source boundary. In this paper we introduce an extension of the QBX scheme in 2D denoted AQBX - adaptive quadrature by expansion - which combines QBX with an algorithm for automated selection of parameters, based on a target error tolerance. A key component in this algorithm is the ability to accurately estimate the numerical errors in the coefficients of the expansion. Combining previous results for flat panels with a procedure for taking the panel shape into account, we derive such error estimates for arbitrarily shaped boundaries in 2D that are discretized using panel-based Gauss-Legendre quadrature. Applying our scheme to numerical solutions of Dirichlet problems for the Laplace and Helmholtz equations, and also for solving these equations, we find that the scheme is able to satisfy a given target tolerance to within an order of magnitude, making it useful for practical applications. This represents a significant simplification over the original QBX algorithm, in which choosing a good set of parameters can be hard