检索结果-内蒙古大学图书馆

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Weinberg, Daniel Hull, Olivia A. Clary, Jacob M. Sundararaman, Ravishankar Vigil-Fowler, Derek Del Ben, Mauro Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Materials Chemical and Computational Science Directorate National Renewable Energy Laboratory GoldenCO United States Department of Materials Science and Engineering Rensselaer Polytechnic Institute TroyNY United States

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation. Copyright © 2024, The Authors. All rights reserved.

关键词： Supercomputers

Optimizing Hammerstein-Wiener Model for Forecasting Confirmed Cases of Covid-19

学校读者我要写书评

暂无评论

IAENG International Journal of applied mathematics 2022年第1期52卷 1页

作者： Abdullahi, Sunusi Bala Ibrahim, Abdulkarim Hassan Abubakar, Auwal Bala Kambheera, Abhiwat General Investigation Zonal Criminal Investigation Section Force Criminal Investigation and Intelligence Department Nigeria Police Abuja900211 Nigeria Department of Applied Mathematics King Mongkut’s University of Technology Thonburi Bangkok Thailand Department of Mathematical Sciences Faculty of Physical Sciences Bayero University Kano700241 Nigeria Mathematics and Computing Science Program Faculty of Science and Technology Phetchabun Rajabhat University Phetchabun 67000 Thailand

Noise poses challenge to nonlinear Hammerstein-Wiener (HW) subsystem model application, because HW subsystem need large number of parameter interactions. However, flexibility, soft computing, and automatic adjustment to dynamic observation for best model fitting make it potential for forecasting nonlinear data. In this article, we adopted improved HW inference from Levenberg-Marquardt optimization algorithm to optimize HW subsystem and to select best model parameters. Therefore, the adopted model is tested on COVID-19 confirmed reported cases, to estimate transmission rate of COVID-19 virus for period from 15th March 2020 to 29th April 2020. Model validation is carried out on small dataset, which outperforms some existing models. The adopted model is further evaluated using statistical metrics and reported best accuracy of 0.127 and 0.998 for Mean Absolute percentage error (MAPE) and coefficient of determination (R2) respectively, with best model complexity of 1.86. The obtained results are promising enough in predicting spread of COVID-19 virus and may inspire as guidance to relax lockdown restriction policies. © 2022, IAENG International Journal of applied mathematics. All Rights Reserved.

关键词： COVID-19

A Lagrangian Method for Reactive Transport with Solid/Aqueous Chemical Phase Interaction i

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Schmidt, Michael J. Pankavich, Stephen D. Navarre-Sitchler, Alexis Benson, David A. Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States

A significant drawback of Lagrangian (particle-tracking) reactive transport models has been their inability to properly simulate interactions between solid and liquid chemical phases, such as dissolution and precipitation reactions. This work addresses that problem by implementing a mass-transfer algorithm between mobile and immobile sets of particles that allows aqueous species of reactant that are undergoing transport to interact with stationary solid species. This mass-transfer algorithm is demonstrated to solve the diffusion equation for an arbitrarily small level of diffusion and thus does not introduce any spurious mixing. The algorithm can be combined with random walks to simulate the desired total level of diffusion in a reactive transport system. Copyright © 2018, The Authors. All rights reserved.

关键词： Diffusion

Neural-PDE: A RNN based neural network for solving time dependent PDEs

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Hu, Yihao Zhao, Tong Xu, Shixin Lin, Lizhen Xu, Zhiliang Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46545 United States Department of Computer Science and Engineering University of Notre Dame Notre DameIN46545 United States Duke Kunshan University Jiangsu Kunshan215316 China

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is frequently a challenging task. Inspired by the traditional finite difference and finite elements methods and emerging advancements in machine learning, we propose a sequence-to-sequence learning (Seq2Seq) framework called Neural-PDE, which allows one to automatically learn governing rules of any time-dependent PDE system from existing data by using a bidirectional LSTM encoder, and predict the solutions in next n time steps. One critical feature of our proposed framework is that the Neural-PDE is able to simultaneously learn and simulate all variables of interest in a PDE system. We test the Neural-PDE by a range of examples, from one-dimensional PDEs to a multi-dimensional and nonlinear complex fluids model. The results show that the Neural-PDE is capable of learning the initial conditions, boundary conditions and differential operators defining the initial-boundary-value problem of a PDE system without the knowledge of the specific form of the PDE system. In our experiments, the Neural-PDE can efficiently extract the dynamics within 20 epochs training and produce accurate predictions. Furthermore, unlike the traditional machine learning approaches for learning PDEs, such as CNN and MLP, which require great quantity of parameters for model precision, the Neural-PDE shares parameters among all time steps, and thus considerably reduces computational complexity and leads to a fast learning algorithm. Copyright © 2020, The Authors. All rights reserved.

关键词： Complex networks

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Kim, Ki-Tae Villa, Umberto Parno, Matthew Marzouk, Youssef Ghattas, Omar Petra, Noemi University of California Merced Applied Mathematics School of Natural Sciences MercedCA United States The University of Texas at Austin Oden Institute for Computational Engineering & Sciences AustinTX United States Dartmouth College Department of Mathematics HanoverNH United States Massachusetts Institute of Technology Department of Aeronautics and Astronautics CambridgeMA United States The University of Texas at Austin Oden Institute for Computational Engineering & Sciences Department of Mechanical Engineering Department of Geological Sciences AustinTX United States

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (∼ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior

关键词： Inverse problems

Erratum to: An efficient forward model of the climate controls on interannual variation in tree-ring width

学校读者我要写书评

暂无评论

Climate Dynamics 2011年第11期36卷 2441-2445页

作者： Susan E. Tolwinski-Ward Michael N. Evans Malcolm K. Hughes Kevin J. Anchukaitis Program in Applied Mathematics University of Arizona Tucson USA Department of Geology University of Maryland College Park USA Laboratory of Tree Ring Research University of Arizona Tucson USA Lamont-Doherty Earth Observatory Columbia University Palisades USA

An Optimal Transport Approach for Network Regression

学校读者我要写书评

暂无评论

An Optimal Transport Approach for Network Regression

Control Technology and Applications (CCTA),

作者： Alex G. Zalles Kai M. Hung Ann E. Finneran Lydia Beaudrot César A. Uribe Department of Computational Applied Mathematics and Operations Research Rice University Houston TX USA Department of Computer Science Rice University Houston TX USA Department of Biosciences Rice University Houston TX USA Department of Electrical and Computer Engineering Rice University Houston TX USA

ISBN: (数字)9798350370942

ISBN: (纸本)9798350370959

We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on Fréchet means and propose a network regression method using the Wasserstein metric. We show that when representing graphs as multivariate Gaussian distributions, the network regression problem requires the computation of a Riemannian center of mass (i.e., Fréchet means). Fréchet means with non-negative weights translates into a barycenter problem and can be efficiently computed using fixed point iterations. Although the convergence guarantees of fixed-point iterations for the computation of Wasserstein affine averages remain an open problem, we provide evidence of convergence in a large number of synthetic and real-data scenarios. Extensive numerical results show that the proposed approach improves existing procedures by accurately accounting for graph size, topology, and sparsity in synthetic experiments. Additionally, real-world experiments using the proposed approach result in higher Coefficient of Determination (R 2 ) values and lower mean squared prediction error (MSPE), cementing improved prediction capabilities in practice.

关键词： Accuracy Network topology computational modeling Cement industry Predictive models Gaussian distribution Aerospace electronics

Note on the gravitational and electromagnetic radiation for the Einstein-Maxwell equations with cosmological constant

学校读者我要写书评

暂无评论

arXiv 2017年

作者： He, Xiaokai Cao, Zhoujian Jing, Jiliang School of Mathematics and Computational Science Hunan First Normal University Changsha Hunan410205 China Department of Physics Hunan Normal University Changsha Hunan410081 China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Physics Key Laboratory of Low Dimensional Quantum Structures Quantum Control of Ministry of Education Synergetic Innovation Center for Quantum Effects and Applications Hunan Normal University Changsha Hunan410081 China

In the middle of last century, Bondi and his coworkers proposed an out going boundary condition for the Einstein equations. Based on such boundary condition the authors theoretically solved the puzzle of the existence problem of gravitational wave. Currently many works on gravitational wave source modeling use Bondi's result to do the analysis including the gravitational wave calculation in numerical relativity. Recently more and more observations imply that the Einstein equations should be modified with an nonzero cosmological constant. In this work we use Bondi's original method to treat the Einstein equations with cosmological constant for theoretical curiosity. We find that the gravitational wave does not essentially exist if Bondi's original out going boundary condition is imposed. We find this unphysical result is due to the non-consistency between Bondi's original out going boundary condition and the Einstein equations with cosmological constant. Based on theoretical analysis, we propose an new Bondi-type out going boundary condition for the Einstein equations with cosmological constant. With this new boundary condition, the gravitational wave behavior for the Einstein equations with cosmological constant is similar to the Einstein equations without cosmological constant. In particular, when the cosmological constant goes to zero, the behavior of the Einstein equations without cosmological constant is recovered. Together with gravitational wave, electromagnetic wave is also analyzed. The boundary conditions for electromagnetic wave does not depend on the cosmological constant. Copyright © 2017, The Authors. All rights reserved.

关键词： Boundary conditions

Original Article: A New Method for Optimal Solution of Intuitionistic Fuzzy Transportation Problems via Generalized Trapezoidal Intuitionistic Fuzzy Numbers

学校读者我要写书评

暂无评论

Fuzzy Information and Engineering 2024年第1期11卷 105-120页

作者： Darunee Hunwisai Poom Kumam Wiyada Kumam Department of Applied Mathematics Faculty of Science and Technology Valaya Alongkorn Rajabhat University under the Royal Patronage Pathumthani Thailand Science Laboratory Building Faculty of Science KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA) Theoretical and Computational Science Center (TaCS) King Mongkut's University of Technology Thonburi (KMUTT) Bangkok Thailand Department of Mathematics and Computer Science Faculty of Science and Technology Rajamangala University of Technology Thanyaburi Pathumthani Thailand

In this paper, we introduce the new method for solving the intuitionistic fuzzy transportation problem (IFTP), by using north-west corner method and modified distribution method to find the optimal solution for IFTP.

关键词： Costs Shape Transportation