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arXiv 2022年

作者： Balan, Radu Haghani, Naveed Singh, Maneesh Department of Mathematics University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States Verisk Analytics Jersey CityNJ07310 United States

This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is invariant to node relabeling. Two embedding schemes are introduced, one based on sorting and the other based on algebras of multivariate polynomials. While both embeddings exhibit a computational complexity exponential in problem size, the sorting based embedding is globally bi-Lipschitz and admits a low dimensional target space. Additionally, an almost everywhere injective scheme can be implemented with minimal redundancy and low computational cost. In turn, this proves that almost any classifier can be implemented with an arbitrary small loss of performance. Numerical experiments are carried out on two data sets, a chemical compound data set (QM9) and a proteins data set (PROTEINS FULL).MSC Codes 05C62, 20C32, 68R12 © 2022, CC BY.

关键词： Embeddings

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Bootstrap Confidence Regions for Directional Data

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Journal of the American Statistical Association 1989年第408期84卷 996-996页

作者： Fisher, Nicholas I. Hall, Peter Program Leader Applied and Industrial Statistics Division of Mathematics and Statistics Commonwealth Scientific and Industrial Research Organisation Lindfield New South Wales 2070 Australia. Professor Department of Statistics Australian National University Canberra Australian Capital Territory 2601 Australia

Methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p-dimensional unit vector X with an arbitrary unimodal distribution on the p sphere. The approach of this article differs from that of other authors in that it is based on pivotal statistics. A general pivotal method is introduced that produces a wide variety of confidence regions on general p-dimensional spheres; included are confidence cones and likelihood-based regions. It can readily be modified to incorporate extra assumptions about the underlying distribution, such as rotational symmetry. The general method leads to confidence pictures, which present information about the estimated posterior likelihood of mean orientation by shading spherical surfaces. An application is given to a sample of spherical cross-bed measurements. The methods extend to the case where X has random length, and to calculation of confidence regions for reference directions of axial bipolar or girdle distributions. [ABSTRACT FROM AUTHOR]

关键词： Axial data Circular data Confidence picture Gray-level image Pivotal statistic Studentization Weighted vectors.

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Low-rank solution methods for stochastic eigenvalue problems

arXiv

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arXiv 2018年

作者： Elman, Howard C. Su, Tengfei Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics & Statistics Scientific Computation Program University of Maryland College ParkMD20742 United States

We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as generalized polynomial chaos expansions. A low-rank variant of the inverse subspace iteration algorithm is presented for computing one or several minimal eigenvalues and corresponding eigenvectors of parameter-dependent matrices. In the algorithm, the iterates are approximated by low-rank matrices, which leads to significant cost savings. The algorithm is tested on two benchmark problems, a stochastic diffusion problem with some poorly separated eigenvalues, and an operator derived from a discrete stochastic Stokes problem whose minimal eigenvalue is related to the inf-sup stability constant. Numerical experiments show that the low-rank algorithm produces accurate solutions compared to the Monte Carlo method, and it uses much less computational time than the original algorithm without low-rank approximation. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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An Assessment of the Supremizer and Aggregation Methods of Stabilization for Reduced-Order Models

arXiv

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arXiv 2023年

作者： Davie, Kayla D. Elman, Howard C. Applied Mathematics & Statistics Scientific Computation Program University of Maryland College ParkMD20742 United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States

MSC Codes 65N22, 65K10, 65F45We explore the features of two methods of stabilization, aggregation and supremizer methods, for reduced-order modeling of parametrized optimal control problems. In both methods, the reduced basis spaces are augmented to guarantee stability. For the aggregation method, the reduced basis approximation spaces for the state and adjoint variables are augmented in such a way that the spaces are identical. For the supremizer method, the reduced basis approximation space for the state-control product space is augmented with the solutions of a supremizer equation. We implement both of these methods for solving several parametrized control problems and assess their performance. Results indicate that the number of reduced basis vectors needed to approximate the solution space to some tolerance with the supremizer method is much larger, possibly double, that for aggregation. There are also some cases where the supremizer method fails to produce a converged solution. We present results to compare the accuracy, efficiency, and computational costs associated with both methods of stabilization which suggest that stabilization by aggregation is a superior stabilization method for control problems. © 2023, CC BY.

关键词： Stabilization

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A Low-rank solver for the stochastic unsteady navier-stokes problem

arXiv

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arXiv 2019年

作者： Elman, Howard Su, Tengfei Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics & Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

We study a low-rank iterative solver for the unsteady Navier–Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once formulation where the algebraic systems at all the time steps are collected and solved simultaneously. The problem is linearized with Picard’s method. To efficiently solve the linear systems at each step, we use low-rank tensor representations within the Krylov subspace method, which leads to significant reductions in storage requirements and computational costs. Combined with effective mean-based preconditioners and the idea of inexact solve, we show that only a small number of linear iterations are needed at each Picard step. The proposed algorithm is tested with a model of flow in a two-dimensional symmetric step domain with different settings to demonstrate the computational efficiency. Copyright © 2019, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Impact of Activation Energy and Chemical Reaction of a 2-Dimensional Rotational Ternary Hybrid Nanofluid Flow of Morphology, Motile Microorganism, Magnetohydrodynamic (MMM) Over a Double Porous Surface

SSRN

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SSRN 2023年

作者： Raza, Qadeer Wang, Xiaodong Chamkha, Ali J. School of Mathematics and Statistics Xi’an Key Laboratory of Scientific Computation and Applied Statistics Northwestern Polytechnical University Xi’an710129 China Faculty of Engineering Kuwait College of Science and Technology Doha District Kuwait35004 Kuwait

The investigation circulates the morphology effect of the activation energy and chemical reaction parameters in two-dimensional rotational ternary hybrid MHD nanofluids flow across through a permeable surface. The phenomenon of heat and mass transfer not only plays a vital role in designing industrial process equipment such as heat exchangers, HVAC types of equipment, and other commercial and consumer products, etc but it is also essential in the enrichment of our overall theoretical knowledge of transfer phenomena. Various physical factors attribute to the heat and mass transfer phenomenon. Motile microorganisms gained importance in recent years regarding their study in the field of heat and mass transfer. This study provides a visual analysis through colored plots for attaining the best heat transfer over a double porous plate by varying different physical parameters. Numerical solutions to nonlinear systems of equations are achieved using the shooting technique. Tables and graphs show how the governing parameters influence velocity, temperature, mass concentration profiles, and motile microorganisms, as well as physical quantities such as skin friction coefficient and Nusselt number. The study will further have great implications in various fields such as coolant technology in the manufacturing sector, heat dissipation in electronic modules, HPC cooling facilities, the automotive industry, and space applications. © 2023, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

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Regulation of systemic risk through contributory endogenous agent-based modeling 14

Regulation of systemic risk through contributory endogenous ...

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Simulation Winter Conference

作者： Aurora J. Bristor Sean L. Barnes Michael C. Fu Applied Mathematics Statistics and Scientific Computation University of Maryland College Park MD USA Robert H. Smith School of Business University of Maryland College Park MD USA

The Financial Stability Oversight Council (FSOC) was created to identify and respond to emerging threats to the stability of the U.S. financial system. The research arm of the FSOC, the Office of Financial Research, has begun to explore agent-based models (ABMs) for measuring the emergent threat of systemic risk. We propose an ABM-based regulatory structure that incentivizes the honest participation and data contribution of regulated firms while providing clarity into the actions of the firms as endogenous to the market and driving emergent behavior. We build this scheme onto an existing ABM of a single-asset market to examine whether the structure of this scheme could provide its own benefits to market stabilization. We find that without regulatory intervention, markets acting within this proposed structure experience fewer bankruptcies and lower leverage buildup while returning larger profits for the same amount of risk.

关键词： Mathematical model Data models Noise computational modeling Atmospheric measurements Particle measurements Adaptation models

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Correction to: An exact scalarization method with multiple reference points for bi-objective integer linear optimization problems

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Annals of Operations Research 2021年第1期332卷 1255-1256页

作者： Filho, Angelo Aliano Moretti, Antonio Carlos Pato, Margarida Vaz de Oliveira, Washington Alves Academic Department of Mathematics Federal Technological University of Paraná Apucarama Brazil Institute of Mathematics Statistics and Scientific Computation University of Campinas Campinas Brazil ISEG and CMAFcIO Universidade de Lisboa Lisbon Portugal School of Applied Sciences University of Campinas Limeira Brazil

In this article a part of the context sections has errors due to an incomplete revision for which the authors much apologize.

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A stochastic MPEC approach for grid tariff design with demand-side flexibility

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2023年第3期14卷 707-729页

作者： Askeland, Magnus Burandt, Thorsten Gabriel, Steven A. Energy Systems SINTEF Energy Research Trondheim Norway Department of Electric Power Engineering Norwegian University of Science and Technology Trondheim Norway Workgroup for Infrastructure Policy Technical University of Berlin Berlin Germany The Energy Transportation Environment Department German Institute for Economic Research (DIW Berlin) Berlin Germany Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Trondheim Norway Department of Mechanical Engineering Applied Math and Statistics Scientific Computation Program University of Maryland College Park MD USA

As the end-users increasingly can provide flexibility to the power system, it is important to consider how this flexibility can be activated as a resource for the grid. Electricity network tariffs is one option that can be used to activate this flexibility. Therefore, by designing efficient grid tariffs, it might be possible to reduce the total costs in the power system by incentivizing a change in consumption patterns. This paper provides a methodology for optimal grid tariff design under decentralized decision-making and uncertainty in demand, power prices, and renewable generation. A bilevel model is formulated to adequately describe the interaction between the end-users and a distribution system operator. In addition, a centralized decision-making model is provided for benchmarking purposes. The bilevel model is reformulated as a mixed-integer linear problem solvable by branch-and-cut techniques. Results based on both deterministic and stochastic settings are presented and discussed. The findings suggest how electricity grid tariffs should be designed to provide an efficient price signal for reducing aggregate network peaks.

关键词： Bilevel problem Grid tariffs Mathematical program with equilibrium constraints (MPEC) Uncertainty

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An Unconditionally Energy Stable Numerical Scheme for the Immersed Boundary Finite Element Method

SSRN

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SSRN 2024年

作者： Ma, Pengfei Cai, Li Wang, Xuan Luo, Xiaoyu Gao, Hao Xi’an Key Laboratory of Scientific Computation and Applied Statistics Shaanxi Xi’an710129 China NPU-UoG International Cooperative Lab for Computation and Application in Cardiology Shaanxi Xi’an710129 China School of Mathematics and Statistics Northwestern Polytechnical University Shaanxi Xi’an710129 China School of Mathematics and Statistics University of Glasgow G128QQ United Kingdom

We propose an unconditionally stable numerical discretization scheme for the immersed boundary finite element (IBFE) method in fluid-structure interaction (FSI) problems. The structure is handled in an implicit way and the structure is generalized with thickness, not treated as fiber or membrane. The only specific assumption is the strain energy function of the structure is a convex function with respect to the deformation gradient. Unconditional stability is proved for the semidiscrete approximation in time. Unconditional stability is also proved for the fully discrete approximation with the absence of convective term, which is left aside as a secondary *** then propose an algorithm to solve the numerical discretization scheme. The Navier-Stokes equations are discretized with finite difference method on staggered grid while the solid mechanics equations are discretized with finite element method on simplex mesh. Semi-Lagrangian method is used to handle the convective term. Duality of the interpolation and distribution operators of the immersed boundary method is satisfied through finite element space projection. Most importantly, the structure force term is discretized using the backward Euler scheme, yielding a nonlinear algebraic system solvable through the Jacobian-free Newton-Krylov (JFNK) *** order to validate the effectiveness and accuracy of our scheme, we present various benchmarks and a quasi-static simulation conducted on a three-dimensional real left ventricle model. In addition, numerical results demonstrate stability of our scheme, the time step is greatly improved, both in the presence and absence of the convective term. Our work paves the way for further works on efficient solvers of the immersed boundary finite element method. © 2024, The Authors. All rights reserved.

关键词： Fluid structure interaction

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