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Improved Deep Neural Network Performance Under Dynamic programming Mode

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SSRN

SSRN 2023年

作者： Cabello, Julia García Department of Applied Mathematics Andalusian Research Institute in Data Science and Computational Intelligence University of Granada Spain

For Deep Neural Networks (DNN), the standard gradient-based algorithms may not be efficient because of the raised computational expense resulting from the increase in the number of layers. This paper offers an alternative to the classic training solutions: an in-depth study to find conditions under which the underlying ANN minimisation problem can be addressed from a Dynamic programming (DP) perspective. Specifically, we prove that any ANN with monotonic activation is separable when regarded as a parametric function. Particularly, when the ANN is viewed as a network representation of a dynamical system (as a coupled cell network), we also prove that the transmission-of-signal law is separable provided the activation function is a monotone non-decreasing function. This strategy may have a positive impact on the performance of ANNs by improving their learning accuracy, particularly for DNNs. For our purposes, ANNs are also viewed as universal approximators of continuous functions and as abstract compositions of an even number of functions. This broader representation makes it easier to analyse them from many other perspectives (universal approximation issues, inverse problem solving) leading to a general improvement in knowledge on NNs and their performance. © 2023, The Authors. All rights reserved.

关键词： Deep neural networks

CEM-GMsFEM for Poisson equations in heterogeneous perforated domains

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arXiv 2024年

作者： Xie, Wei Yang, Yin Chung, Eric Huang, Yunqing National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Department of Mathematics The Chinese University of Hong Kong Shatin Hong Kong

In this paper, we propose a novel multiscale model reduction strategy tailored to address the Poisson equation within heterogeneous perforated domains. The numerical simulation of this intricate problem is impeded by its multiscale characteristics, necessitating an exceptionally fine mesh to adequately capture all relevant details. To overcome the challenges inherent in the multiscale nature of the perforations, we introduce a coarse space constructed using the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). This involves constructing basis functions through a sequence of local energy minimization problems over eigenspaces containing localized information pertaining to the heterogeneities. Through our analysis, we demonstrate that the oversampling layers depend on the local eigenvalues, thereby implicating the local geometry as well. Additionally, we provide numerical examples to illustrate the efficacy of the proposed scheme. Copyright © 2024, The Authors. All rights reserved.

关键词： Poisson equation

Research on Computer Big Data Deep Learning Technology in Mechanical Processing 2

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Research on Computer Big Data Deep Learning Technology in Me...

2nd IEEE International Conference on Power, Electronics and Computer Applications, ICPECA 2022

作者： Xu, Yuelin Huang, Sihao Guo, Jialin Dai, Yue Zhu, Zhilin Shenzhen MSU-BIT University Department of Computational Mathematics and Cybernetics Mathematics and Applied Mathematics Guangdong Shenzhen518172 China Shenzhen MSU-BIT University Materials Science and Engineering Guangdong Shenzhen518172 China Shenzhen MSU-BIT University International Economy and Trade Guangdong Shenzhen518172 China

ISBN: (纸本)9781665442763

Aiming at the problems that traditional manufacturing and processing equipment is not closely related to data and information in the production and processing process, and the use and maintenance of equipment relies on manual experience, a new method of equipment intelligence is proposed. There are faults in motor manufacturing during machining. Based on the non-stationary and non-linear nature of the motor signal itself, combined with the characteristics of large amount of motor monitoring data and the advantages of deep learning methods in target recognition, this paper proposes a fault diagnosis method for motor machining based on deep learning. © 2022 IEEE.

关键词： Manufacture

Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study

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IEEE Transactions on Energy Markets, Policy and Regulation

IEEE Transactions on Energy Markets, Policy and Regulation 2024年第1期2卷 40-51页

作者： Ferrando, Robert Pagnier, Laurent Mieth, Robert Liang, Zhirui Dvorkin, Yury Bienstock, Daniel Chertkov, Michael University of Arizona Program in Applied Mathematics and Department of Mathematics TucsonAZ85721 United States Department of Industrial and Systems Engineering at Rutgers University PiscatawayNJ08854 United States Johns Hopkins University Department of Electrical and Computer Engineering BaltimoreMD21218-2625 United States Elec. and Comp. Eng. and Ralph o'Connor Sustainable Energy Institute Department of Civil and Systems Engineering Johns Hopkins University BaltimoreMD21218-2625 United States Columbia University IEOR New YorkNY10027 United States

This article addresses the challenge of efficiently recovering exact solutions to the optimal power flow problem in real-time electricity markets. The proposed solution, named Physics-Informed Market-Aware Active Set learning OPF (PIMA-AS-OPF), leverages physical constraints and market properties to ensure physical and economic feasibility of market-clearing outcomes. Specifically, PIMA-AS-OPF employs the active set learning technique and expands its capabilities to account for curtailment in load or renewable power generation, which is a common challenge in real-world power systems. The core of PIMA-AS-OPF is a fully-connected neural network that takes the net load and the system topology as input. The outputs of this neural network include active constraints such as saturated generators and transmission lines, as well as non-zero load shedding and wind curtailments. These outputs allow for reducing the original market-clearing optimization to a system of linear equations, which can be solved efficiently and yield both the dispatch decisions and the locational marginal prices (LMPs). The dispatch decisions and LMPs are then tested for their feasibility with respect to the requirements for efficient market-clearing results. The accuracy and scalability of the proposed method is tested on a realistic 1814-bus NYISO system with current and future renewable energy penetration levels. © 2023 IEEE.

关键词： Costs

On the Granular Representation of Fuzzy Quantifier-Based Fuzzy Rough Sets

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arXiv 2023年

作者： Theerens, Adnan Cornelis, Chris Computational Web Intelligence Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium

Rough set theory is a well-known mathematical framework that can deal with inconsistent data by providing lower and upper approximations of concepts. A prominent property of these approximations is their granular representation: that is, they can be written as unions of simple sets, called granules. The latter can be identified with "if..., then..." rules, which form the backbone of rough set rule induction. It has been shown previously that this property can be maintained for various fuzzy rough set models, including those based on ordered weighted average (OWA) operators. In this paper, we will focus on some instances of the general class of fuzzy quantifier-based fuzzy rough sets (FQFRS). In these models, the lower and upper approximations are evaluated using binary and unary fuzzy quantifiers, respectively. One of the main targets of this study is to examine the granular representation of different models of FQFRS. The main findings reveal that Choquet-based fuzzy rough sets can be represented granularly under the same conditions as OWA-based fuzzy rough sets, whereas Sugeno-based FRS can always be represented granularly. This observation highlights the potential of these models for resolving data inconsistencies and managing noise. © 2023, CC BY-NC-ND.

关键词： Machine learning

Symmetry groups and invariant solutions of plane Poiseuille flow

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arXiv 2024年

作者： Aghor, Pratik P. Gibson, John F. School of Earth and Atmospheric Sciences Georgia Institute of Technology United States Integrated Applied Mathematics Program Department of Mathematics & Statistics University of New Hampshire United States

Equilibrium, traveling-wave, and periodic-orbit solutions of the Navier-Stokes equations provide a promising avenue for investigating the structure, dynamics, and statistics of transitional flows. Many such invariant solutions have been computed for wall-bounded shear flows, including plane Couette, plane Poiseuille, and pipe flow. However, the organization of invariant solutions is not well understood. In this paper we focus on the role of symmetries in the organization and computation of invariant solutions of plane Poiseuille *** show that enforcing symmetries while computing invariant solutions increases the efficiency of the numerical methods, and that redundancies between search spaces can be eliminated by consideration of equivalence relations between symmetry subgroups. We determine all symmetry subgroups of plane Poiseuille flow in a doubly-periodic domain up to translations by half the periodic lengths and classify the subgroups into equivalence classes, each of which represents a physically distinct set of symmetries and an associated set of physically distinct invariant *** calculate fifteen new traveling waves of plane Poiseuille flow in seven distinct symmetry groups and discuss their relevance to the dynamics of transitional turbulence. We present a few examples of subgroups with fractional shifts other than half the periodic lengths and one traveling wave solution whose symmetry involves shifts by one-third of the periodic lengths. We conclude with a discussion and some open questions about the role of symmetry in the behavior of shear flows. © 2024, CC BY.

关键词： Navier Stokes equations

Data-driven reduced-order modelling for blood flow simulations with geometry-informed snapshots

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arXiv 2023年

作者： Ye, Dongwei Krzhizhanovskaya, Valeria Hoekstra, Alfons G. Mathematics of Imaging & AI Department of Applied Mathematics University of Twente Netherlands Computational Science Lab Informatics Institute Faculty of Science University of Amsterdam Netherlands

Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations. However, the snapshots of the method require to be collected from the same discretisation, which is a straightforward process for physical parameters, but becomes challenging for geometrical problems, especially for those domains featuring unparameterised and unique shapes, e.g. patient-specific geometries. In this work, a data-driven surrogate model is proposed for the efficient prediction of blood flow simulations on similar but distinct domains. The proposed surrogate model leverages group surface registration to parameterise those shapes and formulates corresponding hemodynamics information into geometry-informed snapshots by the diffeomorphisms constructed between a reference domain and original domains. A non-intrusive reduced-order model for geometrical parameters is subsequently constructed using proper orthogonal decomposition, and a radial basis function interpolator is trained for predicting the reduced coefficients of the reduced-order model based on compressed geometrical parameters of the shape. Two examples of blood flowing through a stenosis and a bifurcation are presented and analysed. The proposed surrogate model demonstrates its accuracy and efficiency in hemodynamics prediction and shows its potential application toward real-time simulation or uncertainty quantification for complex patient-specific *** Codes 65Mxx, 68Txx, 76Zxx Copyright © 2023, The Authors. All rights reserved.

关键词： computational fluid dynamics

Estimation of Digamma Distribution Parameters for Random Sample Size

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Moscow University computational mathematics and Cybernetics 2023年第1期47卷 23-32页

作者： Kudryavtsev, A. A. Shestakov, O. V. Department of Computational Mathematics and Cybernetics Moscow State University Moscow Russia Moscow Center for Fundamental and Applied Mathematics Moscow Russia Federal Research Center ‘‘Informatics and Control ’’ Russian Academy of Sciences Moscow Russia

In this paper asymptotic theorems are proved for estimates of the characteristic index, the scale parameter, and the shape and scale parameters for the remaining fixed parameters of the digamma distribution with a random sample size. Particular cases of limit distributions are given in the case when the sample size has a mixed Poisson distribution.

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Optimal transport reveals dynamic gene regulatory networks via gene velocity estimation

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PLoS computational Biology 2025年第5 May期21卷 e1012476页

作者： Zhao, Wenjun Larschan, Erica Sandstede, Björn Singh, Ritambhara Division of Applied Mathematics Brown University ProvidenceRI United States Department of Mathematics University of British Columbia Vancouver Canada Department of Molecular Biology Cell Biology and Biochemistry Center for Computational Molecular Biology Brown University ProvidenceRI United States Department of Computer Science Center for Computational Molecular Biology Brown University ProvidenceRI United States

Inferring gene regulatory networks from gene expression data is an important and challenging problem in the biology community. We propose OTVelo, a methodology that takes time-stamped single-cell gene expression data as input and predicts gene regulation across two time points. It is known that the rate of change of gene expression, which we will refer to as gene velocity, provides crucial information that enhances such inference;however, this information is not always available due to the limitations in sequencing depth. Our algorithm overcomes this limitation by estimating gene velocities using optimal transport. We then infer gene regulation using time-lagged correlation and Granger causality via regularized linear regression. Instead of providing an aggregated network across all time points, our method uncovers the underlying dynamical mechanism across time points. We validate our algorithm on 13 simulated datasets with both synthetic and curated networks and demonstrate its efficacy on 9 experimental data sets. © 2025 Zhao et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

关键词： Transcription