Multiscale Setting Research Articles

On the Efficient and Accurate Non-linear Computational Modeling of Multilayered Bending Plates. State of the Art and a Novel Proposal: The 2D+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\ ext {D}+$$\\end{document} Multiscale Approach

After conducting a comprehensive historical review of presently established methods for computational modeling of multilayered bending plates, the present work introduces a novel 2D multiscale strategy, termed the 2D+ approach. The proposed approach is based on the computational homogenization formalism and is envisaged to serve as an appealing alternative to current methodologies for modeling multilayered plates in bending-dominated situations. Such structural elements involve modern and relevant materials, such as laminated composites characterized by the heterogeneous distribution of low-aspect-ratio layers showing substantial non-linear mechanical behavior across their thickness.Within this proposed approach, the 2D plate mid-plane constitutes the macroscopic scale, while a 1D filament-like Representative Volume Element (RVE), orthogonal to the plate mid-plane and spanning the plate thickness, represents the mesoscopic scale. Such RVE, in turn, is capturing the non-linear mechanical behavior throughout the plate thickness at each integration point of the 2D plate-midplane finite element mesh. The chosen kinematics and discretization at the considered scales are particularly selected to (1) effectively capture relevant aspects of non-linear mechanical behavior in multilayered plates under bending-dominated scenarios, (2) achieve affordable computational times (computational efficiency), and (3) provide accurate stress distributions compared to the corresponding high-fidelity 3D simulations (computational accuracy).The proposed strategy aligns with the standard, first-order, hierarchical multiscale setting, involving the linearization of the macro-scale displacement field along the thickness. It employs an additional fluctuating displacement field in the RVE to capture higher-order behavior, which is computed through a local 1D finite element solution of a Boundary Value Problem (BVP) at the RVE. A notable feature of the presented 2D+ approach is the application of the Hill–Mandel principle, grounded in the well-established physical assumption imposing mechanical energy equivalence in the macro and meso scales. This links the 2D macroscopic plate and the set of 1D mesoscopic filaments, in a weakly-coupled manner, and yields remarkable computational savings in comparison with standard 3D modeling. Additionally, solving the resulting RVE problem in terms of the fluctuating displacement field allows the enforcement of an additional condition: fulfillment of linear momentum balance (equilibrium equations). This results in a physically meaningful 2D-like computational setting, in the considered structural object (multilayered plates in bending-dominated situations), which provides accurate stress distributions, typical of full 3D models, at the computational cost of 2D models.

Reprint of: A forward–backward greedy approach for sparse multiscale learning

Multiscale models are known to be successful in uncovering and representing structure in data at different resolutions. We propose here a feature driven Reproducing Kernel Hilbert Space (RKHS) for which the associated kernel has a weighted multiscale structure. For generating approximations in this space, we provide a practical forward–backward algorithm that is shown to greedily construct a set of basis functions having a multiscale structure which enables sparse efficient representation of the given data and efficient predictions. We provide a detailed analysis of the algorithm including recommendations for selecting algorithmic hyperparameters and estimating probabilistic rates of convergence at individual scales. We also extend this analysis to a multiscale setting, studying the effects of finite scale truncation and quality of solution in the inherent RKHS. In the last section, we analyze the performance of the approach on a variety of simulations and real data sets illustrating the efficiency claims in terms of model quality and data reduction.

A forward–backward greedy approach for sparse multiscale learning

Multiscale models are known to be successful in uncovering and representing structure in data at different resolutions. We propose here a feature driven Reproducing Kernel Hilbert Space (RKHS) for which the associated kernel has a weighted multiscale structure. For generating approximations in this space, we provide a practical forward–backward algorithm that is shown to greedily construct a set of basis functions having a multiscale structure which enables sparse efficient representation of the given data and efficient predictions. We provide a detailed analysis of the algorithm including recommendations for selecting algorithmic hyperparameters and estimating probabilistic rates of convergence at individual scales. We also extend this analysis to a multiscale setting, studying the effects of finite scale truncation and quality of solution in the inherent RKHS. In the last section, we analyze the performance of the approach on a variety of simulations and real data sets illustrating the efficiency claims in terms of model quality and data reduction.

Forecasting Crude Oil Risk Using a Multivariate Multiscale Convolutional Neural Network Model

In light of the increasing level of correlation and dependence between the crude oil markets and the external influencing factors in the related financial markets, we propose a new multivariate empirical decomposition convolutional neural network model to incorporate the external influence of financial markets such as stock market and exchange market in a multiscale setting into the modeling of crude oil market risk movement. We propose a multivariate empirical model decomposition to analyze the finer details of interdependence among risk movement of different markets across different time horizons or scales. We also introduce the convolutional neural network to construct a new nonlinear ensemble algorithm to reduce the estimation bias and improve the forecasting accuracy. We used the major crude oil price data, stock market index, and the euro/United States dollar exchange rate data to evaluate the performance of the multivariate empirical model decomposition convolutional neural network model. The combination of both the multivariate empirical model decomposition and the convolutional neural network model in this paper has produced the risk forecasts with significantly improved risk forecasting accuracy.

Siamese Networks Based Deep Fusion Framework for Multi-Source Satellite Imagery

A critical aim of pansharpening is to fuse coherent spatial and spectral features from panchromatic and multispectral images respectively. This study proposes deep siamese network based pansharpening model as a two-stage framework in a multiscale setting. In the first stage, a siamese network learns a common feature space between panchromatic and multispectral bands. The second stage follows by fusing the output feature maps of the siamese network. The parameters of these two stages are shared across scales in order to add spatial information consistently (across scales). The spectral information is preserved by adding appropriate skip connections from input multispectral image. Multi-level network parameters sharing mechanism in pyramidal reconstruction of pansharpened image, better preserves spatial and spectral details simultaneously. Experimental work carried out using deep siamese network in multi-scale setting (to obtain inter-band similarity among different sensor data) outperforms several latest pansharpening methods.

HyperLoopNet: Hyperspectral image classification using multiscale self-looping convolutional networks

Hyperspectral image (HSI) classification using convolutional neural networks (CNNs) has always been a hot topic in the field of remote sensing. This is owing to the high level feature extraction offered by CNNs that enables efficient encoding of the features at several stages. However, the drawback with CNNs is that for exceptional performance, they need a deeper and wider architecture along with humongous amount of training data, which is often impractical and infeasible. Furthermore, the reliance on just forward connections leads to inefficient information flow that further limits the classification. Hence, to mitigate these issues, we propose a self-looping convolution network for more efficient HSI classification. In our method, each layer in a self-looping block contains both forward and backward connections, which means that each layer is the input and the output of every other layer, thus forming a loop. These loopy connections within the network allow for maximum information flow, thereby giving us a high level feature extraction. The self-looping connections enable us to efficiently control the network parameters, further allowing us to go for a wider architecture with a multiscale setting, thus giving us abstract representation at different spatial levels. We test our method on four benchmark hyperspectral datasets: Two Houston hyperspectral datasets (DFC 2013 and DFC 2018), Salinas Valley dataset and combined Pavia University and Centre datasets, where our method achieves state of the art performance (highest percentage kappa of 87.28%, 71.08%, 99.24% and 68.44% respectively for the four datasets).

Chinese jigsaw: Solving the equity market response to the COVID-19 crisis: Do alternative asset provide effective hedging performance?

Against COVID-19 risks, this paper examines the hedging performance of alternative assets including some financial assets and commodities futures for the Chinese stock market in a multi-scale setting. Dynamic conditional correlations and optimal hedge ratios of the Shanghai stock exchange with Bitcoin, Dow Jones Industrial Average, Gold, WTI, Bonds and VIX returns are estimated before and during the pandemic crisis. In the short-term, the use of wavelet decomposition shows that Bitcoin provides the best hedge to the Shanghai stock market. In the long-term, commodities dominate. Whereas WTI offers the highest hedging effectiveness, Gold ranks second by a slight margin. These results allow investors to choose the highest returns and protecting tail risk during the current sanitary crisis. Our findings suggest particularly more pronounced economic benefit of diversification including alternative financial assets while commodities futures serve as good hedge assets especially during unpredictable crisis like the current sanitary crisis relating to the covid-19.

Lattice Structure Optimization With Orientation-Dependent Material Properties

Abstract Advances in additive manufacturing (AM) techniques have enabled the production of parts with complex internal geometries. However, the layer-based nature of additive processes often results in mechanical properties that vary based on the orientation of the feature relative to the build plane. Lattice structures have been a popular design application for additive manufacturing due to their potential uses in lightweight structural applications. Many recent works have explored the modeling, design, and fabrication challenges that arise in the multiscale setting of lattice structures. However, there remains a significant challenge in bridging the simplified computational models used in the design process and the more complex properties actually realized in fabrication. This study develops a design approach that captures orientation-dependent material properties that have been observed in metal AM processes, while remaining suitable for use in an iterative design process. Exemplar problems are utilized to investigate the potential design changes and performance improvements that can be attained by taking the directional dependence of the manufacturing process into account in the design of lattice structures.

A Hierarchical Error Estimator for the MSFEM for the Eddy Current Problem in 3-D

The aim of this article is to develop an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> hierarchical error estimator for the multiscale finite element method (MSFEM). The MSFEM is used to solve the linear eddy current problem in a stack of iron sheets. It allows for a calculation of the solution without having to resolve each sheet in the finite element mesh. A hierarchical local error estimator for nodal elements and edge elements is adapted to the multiscale setting. The estimator allows for adaptive p-refinement on the coarse multiscale mesh. Numerical examples show an increased order of convergence compared to uniform refinement. The proposed error estimator increases the efficiency of the MSFEM, requiring even fewer degrees of freedom. It is the first error estimator presented for the 3-D MSFEM for the eddy current problem.

Governance networks around grasslands with contrasting management history

Romanian grasslands have high nature value, being among the most important biodiversity hotspots at the European level. The European Union Common Agricultural Policy (CAP) contradicts the Biodiversity Strategy to 2020 objectives by hindering coordinated grassland governance and collaboration among the involved actors. At the European level, few attempts have been made in creating conceptual strategies for implementing conservation measures in a multi-actor and multi-scale governance setting. Our paper focuses on a comparative network analysis of grassland governance of three Romanian regions (Iron Gates Natural Park – SW; Sighisoara - Tarnava Mare – center; and Dobrogea - SE), representatives for grassland management in mountain and lowland landscapes. We investigated the structural characteristics of one-mode directed governance networks in the three protected areas (standard cohesion and reciprocity metrics, exponential random graph models), the position of actors participating in networks (node-level centrality metrics), and the perception of CAP influence on grassland governance by farmers benefiting of CAP agri-environmental payments. In Sighisoara, grassland governance has been centralized but biodiversity-friendly, while in Iron Gates, grasslands were traditionally managed through a decentralized, community-level system, and this type of governance continues to date. In Dobrogea, grassland governance was performed in an intensive, centralized state-run management regime during the communist time and by large landowners after the transition period ended. Our findings illustrate the structure of the three governance networks and dissimilar patterns of collaboration, indicating distinct particularities to be considered when exploring barriers to and options for successful governance in traditionally managed grasslands in the context of CAP measures-driven management.

Interpreting stochastic agent-based models of cell death

Linking individual cell behavior to changes on the cell population and ultimately tissue scale is a key step towards connecting in vitro laboratory experiments to clinically relevant organ-scale behavior. For example, understanding how an individual tumor cell’s response to drug treatments propagates to the macroscale could help guide clinical decision making when tumors are located in high stakes regions. Based on how dying cells interact, macroscale tumor response can be dominated by tumor shrinkage, tumor damage, change in tumor porosity, or some combination of these phenomena. Here we focus on methods of modeling collective cell behavior with the overall goal of understanding how stochastic cell behavior will ultimately manifest on the cell population scale. To do this, we define and implement an agent-based model problem, introduce novel methods for interpreting simulation results, implement a recently developed technique for conducting a variance-based sensitivity analysis, and investigate key model parameters. Operating within an in silico framework allows us to compare our proposed methods with and without reproducible stochastic variations. This is critical because methods that will be functional for interpreting experimental data must also be able to function when aspects of stochastic variation are not reproducible. To demonstrate the utility of our proposed methods, we identify important simulation parameters for our agent-based model, show that two-dimensional and three-dimensional results are not directly equivalent, and highlight the macroscale implications of cell shrinkage. Looking forward, we anticipate that the methods and results presented here will contribute to significant future research in modeling stochastic cell behavior in the multiscale setting.

A multiscale FE-FFT framework for electro-active materials at finite strains

The present work addresses the fast-Fourier-transform-based computational homogenization of electro-mechanically coupled materials at finite strains. While the macroscopic boundary value problem is solved with finite elements, the solution at microscale is carried out using fast Fourier transforms (FFT). In the context of the FFT-based solution, we propose a general formulation that employs a fully coupled reference medium resulting in fully coupled preconditioning. In order to arrive at an efficient multiscale setting, we provide an algorithmically consistent macroscopic tangent operator for nonlinear electro-mechanical problems derived from the Lippmann–Schwinger equation. We demonstrate the applicability and accuracy of the formulation with some numerical examples. Here, we also investigate both the fully coupled and uncoupled preconditioning as well as the respective impact on the algorithmic solution. It turns out that while the fully coupled scheme leads to quadratic convergence rates, the uncoupled scheme may allow for shorter computation times under certain boundary conditions.

Multiscale convergence properties for spectral approximations of a model kinetic equation

In this work, we prove rigorous convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalent to a standard spectral method in the velocity variable of the kinetic distribution and, as such, is accompanied by standard algebraic estimates of the form $N^{-q}$, where $N$ is the number of modes and $q>0$ depends on the regularity of the solution. However, in the multiscale setting, the error estimate can be expressed in terms of the scaling parameter $\epsilon$, which measures the ratio of the mean-free-path to the characteristic domain length. We show that, for isotropic initial conditions, the error in the spectral approximation is $\mathcal{O}(\epsilon^{N+1})$. More surprisingly, the coefficients of the expansion satisfy super convergence properties. In particular, the error of the $\ell^{th}$ coefficient of the expansion scales like $\mathcal{O}(\epsilon^{2N})$ when $\ell =0$ and $\mathcal{O}(\epsilon^{2N+2-\ell})$ for all $1\leq \ell \leq N$. This result is significant, because the low-order coefficients correspond to physically relevant quantities of the underlying system. All the above estimates involve constants depending on $N$, the time $t$, and the initial condition. We investigate specifically the dependence on $N$, in order to assess whether increasing $N$ actually yields an additional factor of $\epsilon$ in the error. Numerical tests will also be presented to support the theoretical results.

Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier–Stokes equations

This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier–Stokes equations. The framework of the methodology and the correct-energy concept have been developed in the convective–diffusive context in the preceding paper [M.F.P. ten Eikelder, I. Akkerman, Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective–diffusive context, Comput. Methods Appl. Mech. Engrg. 331 (2018) 259–280]. The current work extends ideas of the preceding paper to build a stabilized method within the variational multiscale (VMS) setting which displays correct-energy behavior. Similar to the convection–diffusion case, a key ingredient is the proper dynamic and orthogonal behavior of the small-scales. This is demanded for correct energy behavior and links the VMS framework to the streamline-upwind Petrov–Galerkin (SUPG) and the Galerkin/least-squares method (GLS).The presented method is a Galerkin/least-squares formulation with dynamic divergence-free small-scales (GLSDD). It is locally mass-conservative for both the large- and small-scales separately. In addition, it locally conserves linear and angular momentum. The computations require and employ NURBS-based isogeometric analysis for the spatial discretization. The resulting formulation numerically shows improved energy behavior for turbulent flows comparing with the original VMS method.

Do commodities effectively hedge real estate risk? A multi-scale asymmetric DCC approach

We examine the hedging performance of commodities futures for US real estate portfolios in a multi-scale setting. Dynamic asymmetric conditional correlations and thereafter optimal hedge ratios of real estate stock returns with commodities index, gold, oil and bond returns are estimated to examine hedge effectiveness under heterogeneous market expectations. Rolling window based out-of-sample one-step-ahead forecasts show that commodities index (gold) provide the best hedge to US real estate stocks for short-term (long-term) investments. The results are robust to the choice of model refits and rolling window sizes and provide useful implications for alternate markets’ investors.

Adaptive Bernstein–von Mises theorems in Gaussian white noise

We investigate Bernstein-von Mises theorems for adaptive nonparametric Bayesian procedures in the canonical Gaussian white noise model. We consider both a Hilbert space and multiscale setting with applications in $L^2$ and $L^\infty$ respectively. This provides a theoretical justification for plug-in procedures, for example the use of certain credible sets for sufficiently smooth linear functionals. We use this general approach to construct optimal frequentist confidence sets based on the posterior distribution. We also provide simulations to numerically illustrate our approach and obtain a visual representation of the geometries involved.

A multi-scale high-resolution analysis of global sea surface temperature

The Multi-scale Ultra-high Resolution (MUR) sea surface temperature (SST) analysis presents daily SST estimates on a global 0.01°×0.01° grid. The current version (Version 4.1, http://dx.doi.org/10.5067/GHGMR-4FJ04) features the 1-km resolution MODIS retrievals, which are fused with AVHRR GAC, microwave, and in-situ SST data by applying internal correction for relative biases among the data sets. Only the night-time (dusk to dawn locally) satellite SST retrievals are used to estimate the foundation SST. The MUR SST values agree with the GHRSST Multi-Product Ensemble (GMPE) SST field to 0.36°C on average, except in summer-time Arctic region where the existing SST analysis products are known to disagree with each other. The feature resolution of the MUR SST analysis is an order of magnitude higher than most existing analysis products.The Multi-Resolution Variational Analysis (MRVA) method allows the MUR analysis to use multiple synoptic time scales, including a 5-day data window used for reconstruction of mesoscale features and data windows of only few hours for the smaller scale features. Reconstruction of fast evolving small scale features and interpolation over persistent large data voids can be achieved simultaneously by the use of multiple synoptic windows in the multi-scale setting. The MRVA method is also a “mesh-less” interpolation procedure that avoids truncation of the geolocation data during gridding and binning of satellite samples. Future improvements of the MUR SST analysis will include ingestion of day-time MODIS retrievals as well as more recent high-resolution SST retrievals from VIIRS.

Multiscale stochastic prediction of electricity demand in smart grids using Bayesian networks

Demand management in residential buildings is a key component toward sustainability and efficiency in urban environments. The recent advancements in sensor based technologies hold the promise of novel energy consumption models that can better characterize the underlying patterns.In this paper, we propose a probabilistic data-driven predictive model for consumption forecasting in residential buildings. The model is based on Bayesian network (BN) framework which is able to discover dependency relations between contributing variables. Thus, we can relax the assumptions that are often made in traditional forecasting models. Moreover, we are able to efficiently capture the uncertainties in input variables and quantify their effect on the system output. We test our proposed approach to the data provided by Pacific Northwest National Lab (PNNL) which has been collected through a pilot Smart Grid project.We examine the performance of our model in a multiscale setting by considering various temporal (i.e., 15min, hourly intervals) and spatial (i.e., all households in a region, each household) resolutions for analyzing data. Demand forecasting at the individual households’ levels is a first step toward designing personalized and targeted policies for each customer. While this is a widely studied topic in digital marketing, few researches have been done in the energy sector. The results indicate that Bayesian networks can be efficiently used for probabilistic energy modeling in residential buildings by discovering the dependencies between variables.

Uniform Approximation of Solutions by Elimination of Intermediate Species in Deterministic Reaction Networks

Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a setting, based on ordinary differential equations, in which the presence of intermediate species has little effect on the overall dynamics of a biological system. The result provides a method to perform model reduction by elimination of intermediate species. We study the problem in a multiscale setting, where the species abundances as well a the reaction rates scale to different orders of magnitudes. The different time and concentration scales are parameterised by a single parameter $N$. We show that a solution to the original reaction system is uniformly approximated on compact time intervals to a solution of a reduced reaction system without intermediates and to a solution of a certain limiting reaction systems, which does not depend on $N$. Known approximation techniques such as the theorems by Tikhonov and Fenichel cannot readily be used in this framework.

Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics.

In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous-time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary distributions can be computed explicitly. In particular, we study continuous-time Markov chain models for biochemical interaction systems with non-mass action kinetics whose network satisfies a certain constraint. Analogous with previous related results, the distributions can be written in product form.