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Convolution Neural Network for Finite Element Analysis of 3D Pipe Stress Distribution 23

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Convolution Neural Network for Finite Element Analysis of 3D...

23rd International Conference on Cyberworlds, CW 2024

作者： Chan, Vei Siang Mohamed, Farhan Jamaludin, Najwa Ayuni Idris, Mohd Yazid Wong, Lih Fong Suri, Mohd Syafiq Mohd Umar, Sarehati Iglesias, Andres Universiti Teknologi Malaysia Media and Game Innovation Center of Excellence Johor Bahru Malaysia Universiti Teknologi Malaysia Faculty of Computing Johor Bahru Malaysia Universiti Teknologi Malaysia Faculty of Civil Engineering Johor Bahru Malaysia Universidad de Cantabria Dept. of Applied Mathematics and Computational Sciences Santander Spain Toho University Faculty of Pharmaceutical Sciences Funabashi Japan

ISBN: (纸本)9798331527174

Pipeline analysis plays an essential role in ensuring the structural integrity and safe operation of these critical components. Finite Element Analysis is the commonly used method for assessing stress distribution in pipelines. However, it can be computationally expensive and time-consuming, necessitating alternative approaches. The use of machine learning offers a promising alternative by providing a faster and more efficient approach to predicting stress distribution. This paper shows a prototype focused on the development of a stress distribution surrogate prediction model using an encoder-decoder-based convolutional neural network to analyze the stress distribution of a 3D cylindrical pipe. The related works and methodology are discussed. Then, the results of the study are presented, followed by main conclusions and ideas for future work. © 2024 IEEE.

关键词： Convolutional neural networks

Correction to: The continuous stochastic gradient method: part II–application and numerics

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Computational Optimization and Applications 2023年第3期87卷 1009-1010页

作者： Grieshammer, Max Pflug, Lukas Stingl, Michael Uihlein, Andrian Department of Mathematics Chair of Applied Mathematics Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) Erlangen Germany FAU Competence Center Scientific Computing Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) Erlangen Germany

A Medical Pre-diagnosis Scheme Based on Neural Network and Inner Product Function Encryption

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A Medical Pre-diagnosis Scheme Based on Neural Network and I...

Electronic Communication and Artificial Intelligence (IWECAI), International Workshop on

作者： Xu Cui Hao Liu Min Tang Yihong Ma School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin China Center for Applied Mathematics of Guangxi (GUET) Guilin China

Artificial neural networks are widely used in various fields, such as intelligent road networks, Internet of Things, and smart medical systems due to their ability to process large amounts of data in parallel, store information in a distributed manner, and self-organize and self-learn. Cloud computing technology has further expanded the development of neural network applications. However, user data often contains sensitive information, and once the data management right is transferred to the cloud, it faces serious security and privacy issues. In the medical field, privacy-preserving implementation of classification algorithms is crucial for ensuring the privacy of electronic medical diagnosis services. Current privacy-preserving medical pre-diagnosis schemes based on homomorphic encryption impose a significant computational and communication burden on users and servers. This paper proposes an efficient privacy-preserving medical pre-diagnosis scheme based on neural networks and inner product function encryption that protects user privacy during pre-diagnosis while having small computational and communication overheads.

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WgLaSDI: Weak-Form Greedy Latent Space Dynamics Identification

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arXiv 2024年

作者： He, Xiaolong Tran, April Bortz, David M. Choi, Youngsoo ANSYS Inc. LivermoreCA94551 United States Department of Applied Mathematics University of Colorado BoulderCO80309 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. To enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared to the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5-10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1-7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1,779× speed-up. Copyright © 2024, The Authors. All rights reserved.

关键词： Learning systems

Efficient Deterministic Algorithms for Maximizing Symmetric Submodular Functions

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arXiv 2024年

作者： Wan, Zongqi Zhang, Jialin Sun, Xiaoming Zhang, Zhijie State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences China School of Computer Science and Technology University of Chinese Academy of Sciences China Center for Applied Mathematics of Fujian Province School of Mathematics and Statistics Fuzhou University China

Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio of 0.432 [16]. The algorithm applies the canonical continuous greedy technique that involves a sampling process. It, therefore, suffers from high query complexity and is inherently randomized. In this paper, we present several efficient deterministic algorithms for maximizing a symmetric submodular function under various constraints. Specifically, for the cardinality constraint, we design a deterministic algorithm that attains a 0.432 ratio and uses O(kn) queries. Previously, the best deterministic algorithm attains a 0.385 − ǫ ratio and uses O ( kn(109ǫ ) 20 9ǫ −1) queries [12]. For the matroid constraint, we design a deterministic algorithm that attains a 1/3 − ǫ ratio and uses O(kn log ǫ−1) queries. Previously, the best deterministic algorithm can also attains 1/3 − ǫ ratio but it uses much larger O(ǫ−1n4) queries [24]. For the packing constraints with a large width, we design a deterministic algorithm that attains a 0.432 − ǫ ratio and uses O(n2) queries. To the best of our knowledge, there is no deterministic algorithm for the constraint previously. The last algorithm can be adapted to attain a 0.432 ratio for single knapsack constraint using O(n4) queries. Previously, the best deterministic algorithm attains a 0.316 − ǫ ratio and uses Oe(n3) queries [2]. Copyright © 2024, The Authors. All rights reserved.

关键词： Approximation algorithms

Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging

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arXiv 2024年

作者： Haas, Manuel Grandits, Thomas Pinetz, Thomas Beiert, Thomas Pezzuto, Simone Effland, Alexander Institute of Applied Mathematics University of Bonn Germany Euler Institute Università della svizzera italiana Switzerland Department of Mathematics and Scientific Computing University of Graz Austria Heart Center Bonn Department of Internal Medicine II University Hospital Bonn Germany Department of Mathematics University of Trento Italy

Reconstructing cardiac electrical activity from body surface electric potential measurements results in the severely ill-posed inverse problem in electrocardiography. Many different regularization approaches have been proposed to improve numerical results and provide unique results. This work presents a novel approach for reconstructing the epicardial potential from body surface potential maps based on a space-time total variation-type regularization using finite elements, where a first-order primal-dual algorithm solves the underlying convex optimization problem. In several numerical experiments, the superior performance of this method and the benefit of space-time regularization for the reconstruction of epicardial potential on two-dimensional torso data and a three-dimensional rabbit heart compared to state-of-the-art methods are demonstrated. © 2024, CC BY.

关键词： Convex optimization

SPECTRAL-REFINER: ACCURATE FINE-TUNING OF SPATIOTEMPORAL FOURIER NEURAL OPERATOR FOR TURBULENT FLOWS

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arXiv 2024年

作者： Cao, Shuhao Brarda, Francesco Li, Rui Peng Xi, Yuanzhe School of Science and Engineering University of Missouri Kansas City United States Department of Mathematics Emory University United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States

Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training expenses, and may not always achieve the desired accuracy required in many scientific and engineering disciplines. In this paper, we propose a new learning framework to address these issues. A new spatiotemporal adaptation is proposed to generalize any Fourier Neural Operator (FNO) variant to learn maps between Bochner spaces, which can perform an arbitrary-length temporal super-resolution for the first time. To better exploit this capacity, a new paradigm is proposed to refine the commonly adopted end-to-end neural operator training and evaluations with the help from the wisdom from traditional numerical PDE theory and techniques. Specifically, in the learning problems for the turbulent flow modeled by the Navier-Stokes Equations (NSE), the proposed paradigm trains an FNO only for a few epochs. Then, only the newly proposed spatiotemporal spectral convolution layer is fine-tuned without the frequency truncation. The spectral fine-tuning loss function uses a negative Sobolev norm for the first time in operator learning, defined through a reliable functional-type a posteriori error estimator whose evaluation is exact thanks to the Parseval identity. Moreover, unlike the difficult nonconvex optimization problems in the end-to-end training, this fine-tuning loss is convex. Numerical experiments on commonly used NSE benchmarks demonstrate significant improvements in both computational efficiency and accuracy, compared to end-to-end evaluation and traditional numerical PDE solvers under certain conditions. The source code is publicly available at https://***/scaomath/*** Codes 65M70 (Primary), 35Q30, 76M22, 65M50, 68T07 (Secondary) Copyright © 2024, The Authors. All rights reserved.

关键词： Navier Stokes equations

EFFICIENT NONLINEAR MULTISCALE SPECTRAL GFEM applied TO COMPOSITE AEROSPACE STRUCTURES 23

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EFFICIENT NONLINEAR MULTISCALE SPECTRAL GFEM APPLIED TO COMP...

23rd International Conference on Composite Materials, ICCM 2023

作者： Bénézech, J. Seelinger, L. Reinarz, A. Dodwell, T.J. Butler, R. Scheichl, R. Material & Structure Research Centre University of Bath Bath United Kingdom Interdisciplinary Center for Scientific Computing Institute for Applied Mathematics Heidelberg University Heidelberg Germany Department of Computer Science Durham University Durham United Kingdom Institute of Data Science and AI University of Exeter Exeter United Kingdom DigiLab Exeter United Kingdom

Local Rate of Convergence in the Functional Limit Theorem for Increments of a Fractional Brownian Motion

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数学进展 2025年第1期54卷 197-211页

作者： LIU Yonghong DING Ding ZHOU Xia School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilinGuangxi541004P.R.China Center for Applied Mathematics of Guangxi(GUET) GuilinGuangxi541002P.R.China

In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian *** results obtained extend works of Gantert[***.,1993,21(2):1045-1049]and Mon... 详细信息

关键词： fractional Brownian motion increment local functional law of the iterated logarithm large deviation small deviation