Towards Time-Limited H2\mathcal H_2-Optimal Model Order Reduction

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems and hence reduce computational complexity. A particular class of MOR techniques are $\mathcal H_2$-optimal methods such as the iterative rational Krylov subspace algorithm (IRKA) and related schemes. However, these methods are used to obtain good approximations on a infinite time-horizon. Thus, in this work, our main goal is to discuss MOR schemes for time-limited linear systems. For this, we propose an alternative time-limited $\mathcal H_2$-norm and show its connection with the time-limited Gramians. We then provide first-order optimality conditions for an optimal reduced order model (ROM) with respect to the time-limited $\mathcal H_2$-norm. Based on these optimality conditions, we propose an iterative scheme, which, upon convergence, aims at satisfying these conditions approximately. Then, we analyze how far away the obtained ROM due to the proposed algorithm is from satisfying the optimality conditions. We test the efficiency of the proposed iterative scheme using various numerical examples and illustrate that the newly proposed iterative method can lead to a better reduced-order compared to the unrestricted IRKA in the finite time interval of interest

WikiM: Metapaths based Wikification of Scientific Abstracts

In order to disseminate the exponential extent of knowledge being produced in the form of scientific publications, it would be best to design mechanisms that connect it with already existing rich repository of concepts -- the Wikipedia. Not only does it make scientific reading simple and easy (by connecting the involved concepts used in the scientific articles to their Wikipedia explanations) but also improves the overall quality of the article. In this paper, we present a novel metapath based method, WikiM, to efficiently wikify scientific abstracts -- a topic that has been rarely investigated in the literature. One of the prime motivations for this work comes from the observation that, wikified abstracts of scientific documents help a reader to decide better, in comparison to the plain abstracts, whether (s)he would be interested to read the full article. We perform mention extraction mostly through traditional tf-idf measures coupled with a set of smart filters. The entity linking heavily leverages on the rich citation and author publication networks. Our observation is that various metapaths defined over these networks can significantly enhance the overall performance of the system. For mention extraction and entity linking, we outperform most of the competing state-of-the-art techniques by a large margin arriving at precision values of 72.42% and 73.8% respectively over a dataset from the ACL Anthology Network. In order to establish the robustness of our scheme, we wikify three other datasets and get precision values of 63.41%-94.03% and 67.67%-73.29% respectively for the mention extraction and the entity linking phase

Towards time-limited H2-optimal model order reduction

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems and hence reduce computational complexity. A particular class of MOR techniques are H2-optimal methods such as the iterative rational Krylov subspace algorithm (IRKA) and related schemes. However, these methods are used to obtain good approximations on a infinite time-horizon. Thus, in this work, our main goal is to discuss MOR schemes for time-limited linear systems. For this, we propose an alternative time-limited H2-norm and show its connection with the time-limited Gramians. We then provide first-order optimality conditions for an optimal reduced order model (ROM) with respect to the time-limited H2-norm. Based on these optimality conditions, we propose an iterative scheme which upon convergences aims at satisfying these conditions. Then, we analyze how far away the obtained ROM is from satisfying the optimality conditions.We test the efficiency of the proposed iterative scheme using various numerical examples and illustrate that the newly proposed iterative method can lead to a better reduced-order compared to unrestricted IRKA in the time interval of interest