Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets

Abstract—This paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations. The discretization of the governing equations is obtained through a weak formula-tion using biorthogonal wavelet bases as trial and test functions. It is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes. A simple yet effective time–space adaptive al-gorithm capable of selecting the minimal number of unknowns at each time iteration is described. Numerical results show the high degree of adaptivity of the proposed scheme. Index Terms—Electromagnetic (EM) transient analysis, multi-conductor transmission lines (TLs), wavelet transforms. I

High-Dimensional Bayesian Geostatistics

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as "priors" for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has $\sim n$ floating point operations (flops), where $n$ the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings

Multiresolution modeling and simulation of an air-ground combat application

The High Level Architecture (HLA) establishes a common modeling and simulation framework facilitating interoperability and reuse of simulation components. Since 1996, ONERA (French Aeronautics and Space Research Centre) carries out several studies on HLA in order to gain a better understanding of the underlying mechanisms of HLA implementations. The first critical step of this initiative was to develop our own RTI from the HLA specifications. In order to evaluate the cost of making a transition from legacy simulations to HLA, we first developed an HLA federation simulating an air-ground combat involving a set of aircraft's engaged against a surface to air defense system. Current studies on HLA distributed simulation include security, WAN simulations and multiresolution. Conventional simulations represent entities at just one single level of resolution. Multiresolution representation of entities consists in maintaining multiple and concurrent representations of entities. In this paper we address the problem of how HLA services may allow to achieve multiresolution modeling and simulation. Our goal is not to provide a general framework as a basis for designing simulations of entities at different levels of resolution concurrently. We focus on experience feedback we have obtained by migrating a single level resolution HLA federation to a multi-level resolution federation. The selected application is an air-ground combat simulation involving aggregated patrols of aircraft's engaged against a surface to air defense system. In this paper, we briefly describe the air-ground combat simulation application. We then detail the multiresolution representation of entities (patrols and aircraft's), and discuss the chosen mechanisms allowing triggering aggregation from an entity-level representation, and conversely, triggering disaggregation from an aggregate representation. We focus on the HLA services we have selected to maintain several levels of representation concurrently and on methodological issues in designing multiresolution HLA simulations. We have tackled some difficulties and we propose a new HLA service that should make easier the user's task. This multiresolution management service can be added to our RTI or written by using existing HLA services. Finally, future trends are discussed

Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures

A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational efficiency for large multidimensional computations on standard architectures such as powerful workstations. However, the data structure of the original implementation, based on trees of pointers, provides limited opportunities for efficiency enhancements, while posing serious challenges in terms of parallel programming and load balancing. The present contribution proposes a new implementation of the whole set of numerical methods including Radau5 and ROCK4, relying on a fully different data structure together with the use of a specific library, TBB, for shared-memory, task-based parallelism with work-stealing. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions on multi-core and many-core architectures, demonstrating high scalability

Hierarchically Clustered Adaptive Quantization CMAC and Its Learning Convergence

No abstract availabl

Multiresolution Recurrent Neural Networks: An Application to Dialogue Response Generation

We introduce the multiresolution recurrent neural network, which extends the sequence-to-sequence framework to model natural language generation as two parallel discrete stochastic processes: a sequence of high-level coarse tokens, and a sequence of natural language tokens. There are many ways to estimate or learn the high-level coarse tokens, but we argue that a simple extraction procedure is sufficient to capture a wealth of high-level discourse semantics. Such procedure allows training the multiresolution recurrent neural network by maximizing the exact joint log-likelihood over both sequences. In contrast to the standard log- likelihood objective w.r.t. natural language tokens (word perplexity), optimizing the joint log-likelihood biases the model towards modeling high-level abstractions. We apply the proposed model to the task of dialogue response generation in two challenging domains: the Ubuntu technical support domain, and Twitter conversations. On Ubuntu, the model outperforms competing approaches by a substantial margin, achieving state-of-the-art results according to both automatic evaluation metrics and a human evaluation study. On Twitter, the model appears to generate more relevant and on-topic responses according to automatic evaluation metrics. Finally, our experiments demonstrate that the proposed model is more adept at overcoming the sparsity of natural language and is better able to capture long-term structure.Comment: 21 pages, 2 figures, 10 table

Multiscale modelling and identification of a class of lattice dynamical systems

A new multiscale modelling framework is introduced to describe a class of lattice dynamical systems (LDS), which can be used to model natural systems involving multiphysics and the multi-resolution facets of a single spatio-temporal dynamical system. The emphasis of the paper is on the multi-resolution facets, with respect to the spatial domain, of a single spatio-temporal dynamical system by using a Haar wavelet decomposition technique. A multiscale identification method for such systems is then proposed, which can be considered as a dual of the multigrid method. The proposed identification method involves three steps: the system dynamics at some specific scale of interest are identified using a recursive least-squares algorithm; the residual is then projected onto coarser scales using Haar wavelets and the parameter estimation errors are minimized; and finally a coarse correction procedure is applied to the original scale. An outstanding advantage of the proposed identification method is a saving on the computational costs. Numerical examples are provided to demonstrate the application of the proposed new approach