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arXiv 2024年

作者： Mattey, Revanth Ghosh, Susanta Department of Mechanical Engineering-Engineering Mechanics Michigan Technological University MI United States The Center for Data Sciences The Center for Applied Mathematics and Statistics Michigan Technological University MI United States

Allen-Cahn equation is a reaction-diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen-Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space-time approach. To overcome these challenges, we propose solving the L2 gradient flow of the Ginzburg-Landau free energy functional, which is equivalent to the Allen-Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen-Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space-time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulatio

关键词： Partial differential equations

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Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks

arXiv

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arXiv 2024年

作者： Moya, Christian Mollaali, Amirhossein Zhang, Zecheng Lu, Lu Lin, Guang Department of Mathematics Purdue University West LafayetteIN47907 United States School of Mechanical Engineering Purdue University West LafayetteIN47907 United States Department of Mathematics Florida State University TallahasseeFL32304 United States Department of Statistics and Data Science Yale University New HavenCT06511 United States Department of Mathematics and Mechanical Engineering Purdue University West LafayetteIN47907 United States

In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we enhance the uncertainty quantification frameworks (B-DeepONet and Prob-DeepONet) previously proposed by the authors by using split conformal prediction. By combining conformal prediction with our Prob- and B-DeepONets, we effectively quantify uncertainty by generating rigorous confidence intervals for DeepONet prediction. Additionally, we design a novel Quantile-DeepONet that allows for a more natural use of split conformal prediction. We refer to this distribution-free effective uncertainty quantification framework as split conformal Quantile-DeepONet regression. Finally, we demonstrate the effectiveness of the proposed methods using various ordinary, partial differential equation numerical examples, and multi-fidelity learning. © 2024, CC BY.

关键词： Forecasting

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Coin-structured tunable beam shaping assembly design for accelerator-based boron neutron capture therapy for tumors at different depths and sizes

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Nuclear Science and Techniques 2023年第12期34卷 66-76页

作者： Zhao‑Peng Qiao Yao‑Cheng Hu Quan‑Xu Jiang Jing‑Jing Fan Isao Murata Rui‑Rui Liu Bo Wang Sheng Wang Department of Nuclear Science and Technology School of Energy and Power EngineeringXi’an Jiao-Tong UniversityNo.28Xianning West RoadXi’an 710049China XJTU-Huzhou Neutron Science Laboratory Science Valley Medium‑Sized Building#1Huzhou 313000China RIKEN Center for Advanced Photonics RIKENWakoSaitama 351‑0198Japan Division of Sustainable Energy and Environmental Engineering Graduate School of EngineeringOsaka UniversitySuitaOsaka 565‑0871Japan Department of Radiation Oncology and Winship Cancer Institute Emory UniversityAtlantaGAUSA School of Mathematics and Statistics NingBo UniversityNo.818 Fenghua RoadNingbo 315211China

In the past decade,boron neutron capture therapy utilizing an accelerator-based neutron source(ABNS)designed primarily for producing epithermal neutrons has been implemented in the treatment of brain tumors and other *** specifications for designing an epithermal beam are primarily based on the IAEA-TECODC-1223 report,issued in 2001 for reactor neutron *** on this report,the latest perspectives and clinical requirements,we designed an ABNS capable of adjusting the average neutron beam *** design was based on a 2.8 MeV,20 mA proton beam bombarding a lithium target to produce neutrons that were subsequently moderated and tuned through a tunable beam shaping assembly(BSA)which can modify the thicknesses and materials of the coin-shaped moderators,back reflectors,filters,and *** simulation results demonstrated that epithermal neutron beams for deep seated tumor treatment,which were generated by utilizing magnesium fluoride with lengths ranging between 28 and 36 cm as the moderator,possessed a treatment depth of 5.6 cm although the neutron flux peak shifts from 4.5 to 1.0 *** utilizing a thinner moderator,a less accelerated beam power can meet the treatment ***,higher powers reduced the treatment *** contrast,employing a thick moderator can reduce the skin *** scenarios that required relatively low energy neutron beams,the removal of the thermal neutron filter can raise the thermal neutron flux at the beam *** the depth of the dose rate peak could be adjusted between 0.25 and 2.20 cm by combining magnesium fluoride and polyethylene coins of different ***,this device has a better adaptability for the treatment of superficial ***,the tunable BSA provides greater flexibility for clinical treatment than common BSA designs that can only adjust the port size.

关键词： Boron neutron capture therapy(BNCT) Accelerator-based neutron source(ABNS) Beam shaping assembly(BSA) Treatment depth

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Comparison Model for Forecasting the Total Population in Bangkok 9

Comparison Model for Forecasting the Total Population in Ban...

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Joint 9th International Conference on Digital Arts, Media and Technology with 7th ECTI Northern Section Conference on Electrical, Electronics, Computer and Telecommunications engineering, ECTI DAMT and NCON 2024

作者： Tipwong, Nattanicha Jitpattanakul, Anuchit Phaphan, Wikanda Nontapa, Chalermrat Mekruksavanich, Sakorn King Mongkut's University of Technology North Bangkok Faculty of Applied Science Department of Applied Statistics Bangkok10800 Thailand King Mongkut's University of Technology North Bangkok Faculty of Applied Science Department of Mathematics Bangkok10800 Thailand Intelligent and Nonlinear Dynamic Innovations Research Center Thailand Chiang Mai University Faculty of Science Department of Statistics Chiang Mai50200 Thailand Research Group in Statistical Learning and Inference Thailand University of Phayao School of Information and Communication Department of Computer Engineering Phayao56000 Thailand

ISBN: (纸本)9798350318241

The primary aim of this article is to investigate, contrast, and formulate a time series model to predict Bangkok's overall population. In this study, we intend to propose a hybrid model that combines the Autoregressive Moving Integrated Average (ARIMA) model and machine learning techniques, utilizing a Multilayer Perceptron (MLP). Our data source comprises monthly data from 2002 to 2022, totaling 252 data points, obtained from the official registration statistics system of the Registration Administration Office, department of Provincial Administration. This dataset has been divided into two subsets: the first subset covers the years from 2002 to 2021, encompassing 240 data points, which will be used for constructing predictive models. The second subset consists of the data for the year 2022, comprising 12 data points, which will serve as a means to compare the accuracy of various forecasting methods. The evaluation criteria employed for this purpose are the minimum mean absolute error (MAE), the mean square error (MSE) and the mean absolute percentage error (MAPE). Furthermore, we will utilize the Python programming language to facilitate data analysis. © 2024 IEEE.

关键词： Mean square error

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A Lightweight Encryption Method for Preserving E-Healthcare Data Privacy Using Dual Signature on Twisted Edwards Curves 1

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5th International Conference on Computer and Communication Technologies, IC3T 2023

作者： Farhat, Suryya Kumar, Manoj Vaish, Arti Dewangan, Bhupesh Kumar Choudhury, Tanupriya Kotecha, Ketan Department of Applied Science and Humanities ADGITM Delhi110053 India Department of Mathematics and Statistics Gurukula Kangri Vishwavidyalaya Haridwar249404 India Department of Computer Science and Engineering OP Jindal University Raigarh496109 India Lavale Campus Maharashtra Pune412115 India Pune412115 India Research Professor CSE Dept. Graphic Era Deemed to be University Uttarakhand Dehradun248002 India

ISBN: (数字)9789819997077

ISBN: (纸本)9789819997060

Due to covid-19 pandemic, research in e-healthcare system is gaining popularity because in most of the cases e-healthcare system does not require to present patient physically at doctor’s door. The reason behind this is that e-healthcare system eliminates the necessity for patient to travel at healthcare centres for doctor’s prescription or to collect their diseases diagnostic reports. In the present paper, we have proposed an algorithm, which may be capable to provide integrity for e-healthcare data and preserve its privacy also. The proposed scheme combines dual signature with EdDSA. Dual signature looks similar to double signature but it is quite different;it is a technique of coupling to different values of varied natures preserving them anonymous to varied objects securely. From recent research, it has been proved that elliptic curve cryptography is more suitable for resource constraint (lightweight) device when compared with RSA. Being an improvement of ECDSA, EdDSA signature generation is egregious and affordable. Moreover, EdDSA signature verification, being computationally very hard task, cannot be carried out by e-healthcare devices. Although edge computing devices having no operational constraints can easily perform this task. These characteristics make our proposal more elegant, perky, and efficient strategy for e-healthcare system. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

关键词： Diagnosis

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Subspace Interpolation and Indexing on Stiefel and Grassmann Manifolds as a Lightweight Inference Engine

Subspace Interpolation and Indexing on Stiefel and Grassmann...

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2023 IEEE International Conference on Big Data, BigData 2023

作者： Hu, Wenqing Jiang, Tiefeng Kathariya, Birendra Abrol, Vikram Zhang, Jiali Li, Zhu Missouri University of Science and Technology Rolla Department of Mathematics and Statistics Missouri65409 United States University of Minnesota Twin Cities School of Statistics MinneapolisMN55414 United States University of Missouri Kansas City Department of Computer Science & Electrical Engineering Kansas CityMO64110 United States The Chinese University of Hong Hong Kong at Shenzhen Guangdong Shenzhen518172 China

ISBN: (纸本)9798350324457

Subspace Indexing with Interpolation (SIM-I) on Stiefel and Grassmann manifolds is proposed in this work. Given a partition of some original high-dimensional data set, SIM-I is constructed via two steps: in the first step we build linear affinity-aware subspace models based on each partition;in the second step we interpolate between several adjacent linear subspace models constructed in the first step using the 'center of mass' calculation on Stiefel and Grassmann manifolds. Through these two steps, SIM-I builds a globally nonlinear and smoothly regularized low-dimensional embedding model of the original data set. Furthermore, given sufficiently many training samples on the data manifold either labelled by some pre-trained learning model such as Deep Neural Networks (DNNs) or provided with original natural labels, we first apply SIM-I on this data set and then perform nearest-neighbor classification on the resulting low-dimensional embedding. This helps us to build a Lightweight Inference Engine (LIE) carrying similar level of feature extraction by the pre-trained learning model. For DNNs, such LIE can be interpreted as some (nonstandard) shallow neural network with a wide first hidden layer. From this perspective, SIM-I provides a way to exchange deep network for wide but shallow ones and may provide some new insights to interpret DNNs. © 2023 IEEE.

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Event-Triggered Prescribed-Time Observer-Based Globally Consensus Control for High-Order Multiagent Systems

Event-Triggered Prescribed-Time Observer-Based Globally Cons...

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Chinese Automation Congress (CAC)

作者： Zan Li Tianjiao An Bo Dong Xiaogang Dong School of Mathematics and Statistics Changchun University of Technology Changchun China Department of Control Science and Engineering Changchun University of Technology Changchun China

This paper addresses the globally consensus control problem for nonlinear high-order multiagent systems (MASs) under a directed graph. A novel distributed event-triggered prescribed-time observer (EPTO) is first formulated for the followers, and it is able to accurately estimate the information of the leader agent in a prescribed-time interval. Additionally, the event-triggered condition is constructed for each distributed EPTO to avoid continuous transmission of the neighbor states. The prominent feature of this paper is the designed consensus control scheme, which ensures that the closed-loop system achieves globally prescribed-time stability under the control framework of the backstepping technology. The simulation example further verify the effectiveness of the EPTO-based consensus tracking control scheme.

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Intelligence computing for the dynamic of an entropy-optimized hybrid nanofluid system under the impacts of radiation, Joule heating, and energy dissipation

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Waves in Random and Complex Media 2023年

作者： Shoaib, Muhammad Tabassum, Rafia Raja, Muhammad Asif Zahoor Khan, M. Ijaz Khan, M. Riaz Department of Mathematics COMSATS University Islamabad Attock Campus Islamabad Pakistan Future Technology Research Center National Yunlin University of Science and Technology Douliou Taiwan Department of Mathematics and Statistics Riphah International University I-14 Islamabad Pakistan Department of Mechanical Engineering Lebanese American University Beirut Lebanon Department of Mathematics Quaid-I-Azam University Islamabad Pakistan

In this research paper, the main focus is to inspect Entropy generation of MHD Hybrid nanofluid (MHD-HNF) in a rotating system by considering the AI-based method of Levenberg Marquardt with Back-propagated Neural Network (LM-BPNN). The type of flow is magnetohydrodynamic so all the factors which directly affect the flow like radiation, Ohmic/Joule heating and dissipation in energy expression are discussed by the variation of dimensionless parameters. The system of PDEs presenting the entropy optimized hybrid nanofluid in the rotating system is converted into ODEs using the capability of similarity transformation then the simplified version of fluid flow governing system is further solved by using Adam numerical solver for the computation of the reference dataset with the variation of injection/suction parameter, Reynold Number, Hartmann number, rotation parameter, Brinkman number and heat generation. The validation and correctness of the considered model MHD-HNF are examined by training, testing and validation process of LM-BPNN. Regression analysis, histogram for error and mean square error (MSE) results validate the performance analysis of designed LM-BPNN solver. The assessment of LM-BPNN for velocity and temperature with absolute error analysis plotted graphically and numerically as well as sway of influential parameter on entropy generation and Bejan number analysis are also discussed. © 2023 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Mean square error

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A Resource-Rational Process-Level Account of Violation of Stochastic Dominance 44

A Resource-Rational Process-Level Account of Violation of St...

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44th Annual Meeting of the Cognitive Science Society: Cognitive Diversity, CogSci 2022

作者： Xia, Feng Nobandegani, Ardavan S. Shultz, Thomas R. Bhui, Rahul Department of Mathematics & Statistics McGill University Canada Department of Electrical & Computer Engineering McGill University Canada School of Computer Science McGill University Canada Department of Psychology McGill University Canada Sloan School of Management MIT United States

Dominance is widely considered a pillar of rational choice and has played a major role in the history of theorizing and developing models of human decision-making. A wealth of empirical evidence reveals that humans' violation of dominance is both substantial and systematic. But could violation of dominance be given a rational basis? Specifically, could it be understood in terms of the optimal use of limited cognitive resources? In this work, we present the first resource-rational account of stochastic dominance, the most empirically studied version of dominance. Concretely, we show that a resource-rational process model, sample-based expected utility (SbEU), provides a unified account of a broad range of empirical results on violation of stochastic dominance. We discuss the implications of our work for risky decision-making, and more broadly, human rationality. © 2022 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY)

关键词： Decision making

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Optimization of random high-dimensional functions: Structure and algorithms

arXiv

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arXiv 2022年

作者： Auffinger, Antonio Montanari, Andrea Subag, Eliran Department of Mathematics Norhtwestern University United States Department of Electrical Engineering Department of Statistics Stanford University United States Department of Mathematics Weizmann Institute of Science

Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated to leaves of a tree, and the Euclidean distance between them corresponds to the distance along this tree. We survey recent progress towards a rigorous proof of this picture in the context of mixed p-spin spin glass models. We focus in particular on the following topics: (i) The structure of critical points of the Hamiltonian;(ii) The realization of the ultrametric tree as near optima of a suitable TAP free energy;(iii) The construction of efficient optimization algorithm that exploits this picture. Copyright © 2022, The Authors. All rights reserved.

关键词： Hamiltonians

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