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Efficacy of reduced order source terms for a coupled wave-circulation model in the Gulf of Mexico

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arXiv 2023年

作者： Loveland, Mark Meixner, Jessica Valseth, Eirik Dawson, Clint Oden Institute for Computational Engineering and Sciences University of Texas at Austin Oden Institute for Computational Engineering and Sciences The University of Texas at Austin 201 E. 24th St. AustinTX78712 United States College ParkMD United States The Department of Data Science The Norwegian University of Life Science Drøbakveien 31 Ås1433 Norway Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway

During hurricanes, coupled wave-circulation models are critical tools for public safety. The standard approach is to use a high fidelity circulation model coupled with a wave model that uses the most advanced source terms. As a result, the models can be computationally expensive and so this study investigates the potential consequences of using simplified (reduced order) source terms within the wave model component of the coupled wave-circulation model. The trade-off between run time and accuracy with respect to observations is quantified for a set of two storms that impacted the Gulf of Mexico, Hurricane Ike and Hurricane Ida. Water surface elevations as well as wave statistics (significant wave height, peak period, and mean wave direction) are compared to observations. The usage of the reduced order source terms yielded significant savings in computational cost. Additionally, relatively low amounts of additional error with respect to observations during the simulations with reduced order source terms are observed in our computational experiments. However, large changes in global model outputs of the wave statistics were observed based on the choice of source terms particularly near the track of each hurricane. © 2023, CC BY.

关键词： Hurricanes

Efficient Estimation of Sensor Biases for the 3-Dimensional Asynchronous Multi-Sensor System

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arXiv 2021年

作者： Pu, Wenqiang Liu, Ya-Feng Luo, Zhi-Quan Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

An important preliminary procedure in multi-sensor data fusion is sensor registration, and the key step in this procedure is to estimate sensor biases from their noisy measurements. There are generally two difficulties in this bias estimation problem: one is the unknown target states which serve as the nuisance variables in the estimation problem, and the other is the highly nonlinear coordinate transformation between the local and global coordinate systems of the sensors. In this paper, we focus on the 3-dimensional asynchronous multi-sensor scenario and propose a weighted nonlinear least squares (NLS) formulation by assuming that there is a target moving with a nearly constant velocity. We propose two possible choices of the weighting matrix in the NLS formulation, which correspond to classical and weighted NLS estimation and maximum likelihood (ML) estimation, respectively. To address the intrinsic nonlinearity, we propose a block coordinate descent (BCD) algorithm for solving the formulated problem, which alternately updates different kinds of bias estimates. Specifically, the proposed BCD algorithm involves solving linear LS problems and nonconvex quadratically constrained quadratic program (QCQP) problems with special structures. Instead of adopting the semidefinite relaxation technique, we develop a much more computationally efficient algorithm based on the alternating direction method of multipliers (ADMM) to solve the nonconvex QCQP subproblems. The convergence of the ADMM to the global solution of the QCQP subproblems is established under mild conditions. The effectiveness and efficiency of the proposed BCD algorithm are demonstrated via numerical simulations. Copyright © 2021, The Authors. All rights reserved.

关键词： Maximum likelihood estimation

QUASI-LINEAR FRACTIONAL-ORDER OPERATORS IN LIPSCHITZ DOMAINS

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arXiv 2023年

作者： Borthagaray, Juan Pablo Li, Wenbo Nochetto, Ricardo H. Instituto de Matemática y Estadística "Rafael Laguardia" Facultad de Ingeniería Universidad de la República Montevideo Uruguay Institute of Computational Mathematics and Scientific/Engineering Computing The Chinese Academy of Sciences Beijing100190 China Department of Mathematics Institute for Physical Science and Technology University of Maryland College ParkMD20742 United States

We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains Ω of Rd. Our estimates are consistent with the boundary behavior of solutions on smooth domains and apply to fractional p-Laplacians and operators with finite horizon. The proof exploits the underlying variational structure and uses a new and flexible local translation operator. We further apply these regularity estimates to derive novel error estimates for finite element approximations of fractional p-Laplacians and present several simulations that reveal the boundary behavior of solutions. © 2023, CC BY.

关键词： mathematical operators

CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION

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Journal of computational mathematics 2019年第5期37卷 689-703页

作者： Liaoyuan Zeng Yuhong Dai Yakui Huang Institute of Computational Mathematics and Scientific/Engineering Computing State Key Labomtory of Scientific and Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Science Hebei University of TechnologyTianjin 300401 China

The convergence rate of the gradient descent method is considered for unconstrained multi-objective optimization problems (MOP). Under standard assumptions, we prove that the gradient descent method with constant stepsizes converges sublinearly when the objective functions are convex and the convergence rate can be strengthened to be linear if the objective functions are strongly convex. The results are also extended to the gradient descent method with the Armijo line search. Hence, we see that the gradient descent method for MOP enjoys the same convergence properties as those for scalar optimization.

关键词： Multi-objective optimization Gradient descent Convergence rate.

DOTnet 2.0: Deep learning network for diffuse optical tomography image reconstruction

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Intelligence-Based Medicine 2024年 9卷 100133-100133页

作者： Ko, Zhen Yu Gordon Li, Yang Liu, Jiulong Ji, Hui Qiu, Anqi Chen, Nanguang Department of Biomedical Engineering National University of Singapore Singapore Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing China Department of Mathematics National University of Singapore Singapore Department of Biomedical Engineering Johns Hopkins University Baltimore MD United States Department of Health Technology and Informatics The Hong Kong Polytechnic University (PolyU) Hong Kong Hong Kong National University of Singapore (Suzhou) Research Institute Suzhou Industrial Park Jiangsu Suzhou China

Breast cancer is the most common cancer worldwide. The standard imaging modality for breast cancer screening is X-ray mammography, which suffers from low sensitivities in women with dense breasts and can potentially cause cancers despite a low radiation dosage. Diffuse Optical Tomography (DOT) is a noninvasive imaging technique that can potentially be employed to improve breast cancer early detection. However, conventional model-based algorithms for reconstructing DOT images usually produce low-quality images with limited resolution and low reconstruction accuracy. We propose to integrate deep neural networks (DNNs) with the conventional DOT reconstruction methods. This hybrid framework significantly enhances image quality. The DNNs have been trained and tested with sample data derived from clinically relevant breast models. The sample dataset contains blood vessel structures from breast structures and artificially created vessels using the Lindenmayer-system algorithm. By comparing the hybrid reconstruction with the ground truth image, we demonstrated a multi scale - structural similarity index measure (MS-SSIM) score of 0.80–0.90. Whereas using conventional reconstruction, MS-SSIM provided a much inferior score of 0.36–0.59. In terms of DOT image quality, both qualitative and quantitative assessments of the reconstructed images signify that the hybrid approach is superior to conventional methods. This improvement suggests that DOT can potentially become a viable alternative to breast cancer screening, providing a step towards the next-generation device for optical mammography. © 2024 The Authors

关键词： Breast cancer Convolutional neural network Deep learning Diffuse optical tomography Image reconstruction

ERROR ESTIMATE OF MULTISCALE FINITE ELEMENT METHOD FOR PERIODIC MEDIA REVISITED

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arXiv 2022年

作者： Ming, Pingbing Song, Siqi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic systems with rapidly oscillating periodic coefficients that are bounded measurable, which may admit rough microstructures. As a by-product of the energy error estimate, we derive the rate of convergence in Ld/(d−1)−norm with d the dimensionality. © 2022, CC BY.

关键词： Finite element method

Shape of my heart: Cardiac models through learned signed distance functions

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arXiv 2023年

作者： Verhülsdonk, Jan Grandits, Thomas Costabal, Francisco Sahli Pinetz, Thomas Krause, Rolf Auricchio, Angelo Haase, Gundolf Pezzuto, Simone Effland, Alexander Institute for Applied Mathematics University of Bonn Germany Department of Mathematics and Scientific Computing University of Graz Austria Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Chile Center for Computational Medicine in Cardiology Università della Svizzera italiana Switzerland FernUni Schweiz Brig Switzerland Instituto Cardiocentro Ticino EOC Switzerland Department of Mathematics University of Trento Italy

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM). Copyright © 2023, The Authors. All rights reserved.

关键词： Image resolution

Novel Structure-Preserving Schemes for Stochastic Klein-Gordon-Schr\"Odinger Equations with Additive Noise

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SSRN

SSRN 2023年

作者： Hong, Jialin Hou, Baohui Sun, Liying Zhang, Xiaojing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mathematics Shanghai University Shanghai200444 China School of Mathematical Sciences Capital Normal University Beijing100048 China

Stochastic Klein–Gordon–Schr¨odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel structure-preserving schemes to numerically solve stochastic KGS equations with additive noise, which preserve averaged charge evolution law, averaged energy evolution law, symplecticity, and multi-symplecticity. By applying central difference, sine pseudo-spectral method, or finite element method in space and modifying finite difference in time, we present some charge and energy preserved fullydiscrete scheme for the original system. In addition, combining the symplectic Runge-Kutta method in time and finite difference in space, we propose a class of multi-symplectic discretizations preserving the geometric structure of the stochastic KGS equation. Finally, numerical experiments confirm theoretical findings. © 2023, The Authors. All rights reserved.

关键词： Additive noise

Large-Scale Materials Modeling at Quantum Accuracy: Ab Initio Simulations of Quasicrystals and Interacting Extended Defects in Metallic Alloys

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Large-Scale Materials Modeling at Quantum Accuracy: Ab Initi...

Supercomputing Conference

作者： Sambit Das Bikash Kanungo Vishal Subramanian Gourab Panigrahi Phani Motamarri David Rogers Paul M. Zimmerman Vikram Gavini Department of Mechanical Engineering University of Michigan Ann Arbor MI USA Department of Materials Science & Engineering University of Michigan Ann Arbor MI USA Department of Computational and Data Sciences Indian Institute of Science Bangalore Karnataka India Scientific Computing Group Oak Ridge National Laboratory Oak Ridge TN USA Department of Chemistry University of Michigan Ann Arbor MI USA

Ab initio electronic-structure has remained dichotomous between achievable accuracy and length-scale. Quantum many-body (QMB) methods realize quantum accuracy but fail to scale. Density functional theory (DFT) scales favorably but remains far from quantum accuracy. We present a framework that breaks this dichotomy by use of three interconnected modules: (i) invDFT: a methodological advance in inverse DFT linking QMB methods to DFT; (ii) MLXC: a machine-learned density functional trained with invDFT data, commensurate with quantum accuracy; (iii) DFT-FE-MLXC: an adaptive higher-order spectral finite-element (FE) based DFT implementation that integrates MLXC with efficient solver strategies and HPC innovations in FE-specific dense linear algebra, mixed-precision algorithms, and asynchronous compute-communication. We demonstrate a paradigm shift in DFT that not only provides an accuracy commensurate with QMB methods in ground-state energies, but also attains an unprecedented performance of 659.7 PFLOPS (43.1% peak FP64 performance) on 619,124 electrons using 8,000 GPU nodes of Frontier supercomputer.

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