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data simulation of optimal model for numerical solution of differential equations based on deep learning and genetic algorithm

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SOFT COMPUTING 2023年第14期27卷 10025-10032页

作者： Jing, Li Zhengzhou Railway Vocat & Tech Coll Basic Teaching Dept Zhengzhou 450052 Peoples R China

Calculus equation is an important tool for mathematical research and plays an important role in most natural science research. Since the beginning of the eighteenth century, people have gradually used differential and integral equations to solve physical problems. In general, several different aspects of differential equations in the field of mathematics are concerned and studied by most scholars. However, this paper studies and establishes the optimal model for numerical solution of differential equations through deep learning and genetic algorithm. In this paper, the solution of ordinary differential equations is solved through the use of polynomial function space, while the linear combination of simple function x and its product nx can obtain multinomial function space. The space function form of polynomial is very simple, and the operation ability is very strong. Almost all functions can be approximated, and the function space can be transformed by a simple function. Through data simulation test results, it can be found that the oscillation of neural network output is stronger and stronger with the increase in depth, that is to say, the deeper depth endows the neural network with stronger oscillation properties, so for the oscillation function, the depth neural network fitting effect is better than the shallow neural network. Therefore, by combining deep learning and genetic algorithm, this paper studies and establishes the optimal model for numerical solution of differential equations, and finds that the deep neural network can largely complete data simulation.

关键词： Deep learning Genetic algorithm Differential equation numerical solution optimal model data simulation

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Using SEM programs to perform matrix manipulations and data simulation

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STRUCTURAL EQUATION MODELING 2003年第2期10卷 312-322页

作者： Raykov, T Marcoulides, GA Boyd, J Fordham Univ Dept Psychol Bronx NY 10458 USA Calif State Univ Fullerton Fullerton CA 92634 USA

A didactic discussion of a simple method for Cholesky decomposition and obtaining a symmetric square root of a positive definite covariance matrix using popular structural equation modeling programs is discussed. The applicability of such software for purposes of accomplishing some matrix manipulations is demonstrated. The approach can also be used to generate multivariate normal data. The outlined procedure is illustrated with a numerical example.

关键词： .covariance Cholesky LISREL STRUCTURAL EQUATION MODELING reskog rbom Matrix Manipulations data simulation symmetric square normal data

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Optimization of financial market risk prediction system based on computer data simulation and Markov chain Monte Carlo

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SOFT COMPUTING 2023年 1-10页

作者： Yuanfang, Zhang Xian Peihua Univ Sch Accounting & Finance Xian 710125 Shaanxi Peoples R China

With the continuous development of the times, the business scope of the financial market is also expanding, and more and more unknown risks have emerged in the process of development, which has brought a certain impact to the financial market. The exchange rate fluctuation, interest rate and other factors related to the international financial market make financial market risk one of the important risks faced by securities companies. Therefore, securities companies need intuitive, accurate and effective quantitative management tools for financial market risk assessment to improve the overall risk management level of the company. Therefore, this paper constructs a financial market risk prediction system based on computer data simulation technology and Markov chain Monte Carlo algorithm. This system is mainly composed of three parts: financial risk management, data exchange management and background risk application services. The front end of the financial market risk prediction system is divided into risk monitoring, risk allocation, risk report, risk decision-making and system log modules according to functions. data collection management functions mainly include data collection, data encryption, data conversion, data return and other functions. The measured results show that the system can predict the significant inflection points in most economic risks synchronously or in advance, and the forecast data show that the financial security index has an upward trend from bottom to top. In this paper, the Markov chain Monte Carlo algorithm is introduced into the financial market, through data simulation to predict the risks of companies with economic risks and make a small contribution to the market development.

关键词： Markov chain Monte Carlo data simulation Financial market Economic risk Risk assessment

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LASER-DOPPLER ANEMOMETRY data simulation - APPLICATION TO INVESTIGATE THE ACCURACY OF STATISTICAL ESTIMATORS

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AIAA JOURNAL 1994年第9期32卷 1883-1889页

作者： FUCHS, W NOBACH, H TROPEA, C UNIV ERLANGEN NUREMBERG LEHRSTUHL STROMUNGSMECHD-91058 ERLANGENGERMANY

Autoregressive models of order 1 are used to generate three-dimensional flowfields with specified probability distributions, spectra, and shear stress tensor. These known flowfields are then used to simulate the particle arrival statistics in laser Doppler anemometry for homogeneous particle densities. Further simulation steps allow modeling of the processor sampling and data acquisition, providing all necessary data for investigating the bias and variance of statistical estimators. Results are presented for estimators of the first two moments of the velocity distribution function. Experimental data are obtained for verification purposes. The results demonstrate the technique's potential for studying novel or theoretically intractable estimators.

关键词： Laser Doppler Anemometry Normal Stress data Acquisition Power Spectral Density data simulation Velocity Distribution Function Reynolds Stress Separated Flows Numerical simulation Turbulence Intensity

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simrel - A versatile tool for linear model data simulation based on the concept of a relevant subspace and relevant predictors

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2015年 146卷 128-135页

作者： Saebo, Solve Almoy, Trygve Helland, Inge S. Norwegian Univ Life Sci Dept Chem Biotechnol & Food Sci NO-1432 As Norway Univ Oslo Dept Math NO-0316 Oslo Norway

In the field of chemometrics and other areas of data analysis the development of new methods for statistical inference and prediction is the focus of many studies. The requirement to document the properties of new methods is inevitable, and often simulated data are used for this purpose. However, when it comes to simulating data there are few standard approaches. In this paper we propose a very transparent and versatile method for simulating response and predictor data from a multiple linear regression model which hopefully may serve as a standard tool simulating linear model data. The approach uses the principle of a relevant subspace for prediction, which is known both from Partial Least Squares and envelope models, and is essentially based on a re-parametrization of the random x regression model. The approach also allows for defining a subset of relevant observable predictor variables spanning the relevant latent subspace, which is handy for exploring methods for variable selection. The data properties are defined by a small set of input-parameters defined by the analyst. The versatile approach can be used to simulate a great variety of data with varying properties in order to compare statistical methods. The method has been implemented in an R-package and its use is illustrated by examples. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： data simulation Linear model R-package Experimental design

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A finite mixture approach to univariate data simulation with moment matching

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ENVIRONMENTAL MODELLING & SOFTWARE 2017年 90卷 27-33页

作者： Bardsley, Earl Univ Waikato Fac Sci & Engn Private Bag 3105 Hamilton 3240 New Zealand

Environmental data simulation is carried out for various purposes and is most simply achieved when recorded data can be regarded as a sequence of independent random variables. Simulating from such data involves generating random variables from some fitted probability distribution, preserving the main statistical characteristics. The particular case of data simulation with moment matching is revisited, with a proposal that data be simulated from many-component finite mixture distributions. The simulation procedure matches data moments while also giving greater flexibility for data approximation. In contrast, a single parametric distribution fitted to irregular data will result in data simulations more representative of the fitted distribution than the original data. The flexible finite mixture approach therefore has potential to replace parametric univariate data simulation generally. The method is illustrated with simulations from finite mixtures of generalised beta distributions with matching of data mean, variance, skewness and kurtosis. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Moment matching Finite mixture distribution data simulation Beta distribution

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Efficient sampled-data simulation method for transient analysis of nonlinear circuits

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IEE PROCEEDINGS-CIRCUITS DEVICES AND SYSTEMS 2002年第2期149卷 105-111页

作者： Yuan, F Ryerson Univ Dept Elect & Comp Engn Toronto ON M5B 2K3 Canada

The paper presents an explicit and efficient transient analysis method for nonlinear circuits. The method makes use of Volterra series representation of nonlinear systems and characterises the behaviour of nonlinear circuits in the time domain using a set of Volterra circuits. The input of the first-order Volterra circuit is the same as that of the nonlinear circuit, whereas that of higher-order Volterra circuits is obtained from the response of lower-order Volterra circuits and interpolation. These Volterra circuits are solved using the sampled-data simulation of linear circuits for computational efficiency and accuracy. The response of the nonlinear circuit is computed at equally spaced instants of time. Numerical results on example circuits demonstrate that the accuracy of the method is comparable to that of widely used predictor-corrector algorithms, but with greatly improved computational efficiency.

关键词： data sampling Linear circuits Electric circuits analog approach Nonlinear circuits TIME-DOMAIN Transient analysis Computational efficiency Volterra series Nonlinear systems data simulation

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Systematic evaluation with practical guidelines for single-cell and spatially resolved transcriptomics data simulation under multiple scenarios

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GENOME BIOLOGY 2024年第1期25卷 1页

作者： Duo, Hongrui Li, Yinghong Lan, Yang Tao, Jingxin Yang, Qingxia Xiao, Yingxue Sun, Jing Li, Lei Nie, Xiner Zhang, Xiaoxi Liang, Guizhao Liu, Mingwei Hao, Youjin Li, Bo Chongqing Normal Univ Coll Life Sci Chongqing 401331 Peoples R China Chongqing Univ Posts & Telecommun Chongqing Key Lab Big Data Bio Intelligence Chongqing 400065 Peoples R China Army Med Univ Southwest Hosp Inst Pathol Chongqing 400038 Peoples R China Army Med Univ Southwest Hosp Southwest Canc Ctr Chongqing 400038 Peoples R China Zhejiang Univ Womens Hosp Zhejiang Prov Key Lab Precis Diag & Therapy Major Sch Med Hangzhou 310058 Peoples R China Chongqing Univ Bioengn Coll Key Lab Biorheol Sci & Technol Minist Educ Chongqing 400044 Peoples R China Chongqing Med Univ Coll Lab Med Key Lab Clin Lab Diagnost Chongqing 400016 Peoples R China

Background Single-cell RNA sequencing (scRNA-seq) and spatially resolved transcriptomics (SRT) have led to groundbreaking advancements in life sciences. To develop bioinformatics tools for scRNA-seq and SRT data and perform unbiased benchmarks, data simulation has been widely adopted by providing explicit ground truth and generating customized datasets. However, the performance of simulation methods under multiple scenarios has not been comprehensively assessed, making it challenging to choose suitable methods without practical *** We systematically evaluated 49 simulation methods developed for scRNA-seq and/or SRT data in terms of accuracy, functionality, scalability, and usability using 152 reference datasets derived from 24 platforms. SRTsim, scDesign3, ZINB-WaVE, and scDesign2 have the best accuracy performance across various platforms. Unexpectedly, some methods tailored to scRNA-seq data have potential compatibility for simulating SRT data. Lun, SPARSim, and scDesign3-tree outperform other methods under corresponding simulation scenarios. Phenopath, Lun, Simple, and MFA yield high scalability scores but they cannot generate realistic simulated data. Users should consider the trade-offs between method accuracy and scalability (or functionality) when making decisions. Additionally, execution errors are mainly caused by failed parameter estimations and appearance of missing or infinite values in calculations. We provide practical guidelines for method selection, a standard pipeline Simpipe (https://***/duohongrui/simpipe;https://***/10.5281/zenodo.11178409), and an online tool Simsite (https://***/software/simshiny/) for data *** No method performs best on all criteria, thus a good-yet-not-the-best method is recommended if it solves problems effectively and reasonably. Our comprehensive work provides crucial insights for developers on modeling gene expression data and fosters the simulation process for users

关键词： Evaluation Single-cell transcriptomics Spatially resolved transcriptomics data simulation Guideline

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Survivability analysis and data simulation of logistic networks under different attacks

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ANNALS OF OPERATIONS RESEARCH 2022年第1期348卷 147-180页

作者： Dui, Hongyan Cui, Miao Tao, Junyong Bai, Guanghan Zhengzhou Univ Sch Management Zhengzhou 450001 Peoples R China Natl Univ Def Technol Coll Intelligence Sci & Technol Lab Sci & Technol Integrated Logist Support Changsha 410073 Peoples R China

In recent years, the logistic network in combat tends to be complicated with the development of joint operations. When the network is attacked, how to effectively protect it and improve the survivability of the logistic network is vital for the overall performance of the combat system. In this study, the survivability of the logistic network against different attacks is analyzed. Three attack modes are considered, namely random attack, intentional attack, and comprehensive attack with partial information. Network efficiency and effective survival time are defined as the evaluation indexes of the network survivability. Then the importance measure and survivability analysis of the network are carried out. The impact of intentional and random attacks on network survivability in task redistribution mode is calculated. At last, a data simulation is given to demonstrate the proposed method.

关键词： Survivability Logistic networks data simulation Intentional attack

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EFFECTIVE NOISE-AWARE data simulation FOR DOMAIN-ADAPTIVE SPEECH ENHANCEMENT LEVERAGING DYNAMIC STOCHASTIC PERTURBATION

EFFECTIVE NOISE-AWARE DATA SIMULATION FOR DOMAIN-ADAPTIVE SP...

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2024 Spoken Language Technology Workshop

作者： Wang, Chien-Chun Chen, Li-Wei Lee, Hung-Shin Chen, Berlin Wang, Hsin-Min Natl Taiwan Normal Univ Dept Comp Sci & Informat Engn Taipei Taiwan Acad Sinica Inst Comp Sci Taipei Taiwan United Link Co Ltd Taipei Taiwan

ISBN: (纸本)9798350392265;9798350392258

Cross-domain speech enhancement (SE) is often faced with severe challenges due to the scarcity of noise and background information in an unseen target domain, leading to a mismatch between training and test conditions. This study puts forward a novel data simulation method to address this issue, leveraging noise-extractive techniques and generative adversarial networks (GANs) with only limited target noisy speech data. Notably, our method employs a noise encoder to extract noise embeddings from target-domain data. These embeddings aptly guide the generator to synthesize utterances acoustically fitted to the target domain while authentically preserving the phonetic content of the input clean speech. Furthermore, we introduce the notion of dynamic stochastic perturbation, which can inject controlled perturbations into the noise embeddings during inference, thereby enabling the model to generalize well to unseen noise conditions. Experiments on the VoiceBank-DEMAND benchmark dataset demonstrate that our domain-adaptive SE method outperforms an existing strong baseline based on data simulation.

关键词： domain adaptation data simulation data augmentation speech enhancement

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