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排序方式: 共有356条查询结果,搜索用时 15 毫秒
1.
In this paper, we introduce a new type of troubled-cell indicator to improve
hybrid weighted essentially non-oscillatory (WENO) schemes for solving the hyperbolic conservation laws. The hybrid WENO schemes selectively adopt the high-order
linear upwind scheme or the WENO scheme to avoid the local characteristic decompositions and calculations of the nonlinear weights in smooth regions. Therefore,
they can reduce computational cost while maintaining non-oscillatory properties in
non-smooth regions. Reliable troubled-cell indicators are essential for efficient hybrid
WENO methods. Most of troubled-cell indicators require proper parameters to detect
discontinuities precisely, but it is very difficult to determine the parameters automatically. We develop a new troubled-cell indicator derived from the mean value theorem
that does not require any variable parameters. Additionally, we investigate the characteristics of indicator variable; one of the conserved properties or the entropy is considered as indicator variable. Detailed numerical tests for 1D and 2D Euler equations are
conducted to demonstrate the performance of the proposed indicator. The results with
the proposed troubled-cell indicator are in good agreement with pure WENO schemes.
Also the new indicator has advantages in the computational cost compared with the
other indicators. 相似文献
2.
Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning
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Yufei Wang Ziju Shen Zichao Long & Bin Dong 《Communications In Computational Physics》2020,28(5):2158-2179
Conservation laws are considered to be fundamental laws of nature. It has
broad applications in many fields, including physics, chemistry, biology, geology, and
engineering. Solving the differential equations associated with conservation laws is a
major branch in computational mathematics. The recent success of machine learning,
especially deep learning in areas such as computer vision and natural language processing, has attracted a lot of attention from the community of computational mathematics and inspired many intriguing works in combining machine learning with traditional methods. In this paper, we are the first to view numerical PDE solvers as an
MDP and to use (deep) RL to learn new solvers. As proof of concept, we focus on
1-dimensional scalar conservation laws. We deploy the machinery of deep reinforcement learning to train a policy network that can decide on how the numerical solutions should be approximated in a sequential and spatial-temporal adaptive manner.
We will show that the problem of solving conservation laws can be naturally viewed
as a sequential decision-making process, and the numerical schemes learned in such a
way can easily enforce long-term accuracy. Furthermore, the learned policy network
is carefully designed to determine a good local discrete approximation based on the
current state of the solution, which essentially makes the proposed method a meta-learning approach. In other words, the proposed method is capable of learning how to
discretize for a given situation mimicking human experts. Finally, we will provide details on how the policy network is trained, how well it performs compared with some
state-of-the-art numerical solvers such as WENO schemes, and supervised learning
based approach L3D and PINN, and how well it generalizes. 相似文献
3.
We focus on the Fisher information matrix used for design evaluation and optimization in nonlinear mixed effects multiple response models. We evaluate the appropriateness of its expression computed by linearization as proposed for a single response model. Using a pharmacokinetic–pharmacodynamic (PKPD) example, we first compare the computation of the Fisher information matrix with approximation to one derived from the observed matrix on a large simulation using the stochastic approximation expectation–maximization algorithm (SAEM). The expression of the Fisher information matrix for multiple responses is also evaluated by comparison with the empirical information obtained through a replicated simulation study using the first‐order linearization estimation methods implemented in the NONMEM software (first‐order (FO), first‐order conditional estimate (FOCE)) and the SAEM algorithm in the MONOLIX software. The predicted errors given by the approximated information matrix are close to those given by the information matrix obtained without linearization using SAEM and to the empirical ones obtained with FOCE and SAEM. The simulation study also illustrates the accuracy of both FOCE and SAEM estimation algorithms when jointly modelling multiple responses and the major limitations of the FO method. This study highlights the appropriateness of the approximated Fisher information matrix for multiple responses, which is implemented in PFIM 3.0, an extension of the R function PFIM dedicated to design evaluation and optimization. It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
4.
This paper presents the use of iterative dynamic programming employing exact penalty functions for minimum energy control problems. We show that exact continuously non-differentiable penalty functions are superior to continuously differentiable penalty functions in terms of satisfying final state constraints. We also demonstrate that the choice of an appropriate penalty function factor depends on the relative size of the time delay with respect to the final time and on the expected value of the energy consumption. A quadratic approximation (QA) of the delayed variables is much better than a linear approximation (LA) of the same for relatively large time delays. The QA improves the rate of convergence and avoids the formation of ‘kinks‘. A more general way of selecting appropriate penalty function factors is given and the results obtained using four illustrative examples of varying complexity corroborate the efficacy of the method. 相似文献
5.
Jared Liu Hsin-Wen Chang Zhi-Ming Huang Mio Nakamura Sahil Sekhon Richard Ahn Priscila Munoz-Sandoval Shrishti Bhattarai Kristen M. Beck Isabelle M. Sanchez Eric Yang Mariela Pauli Sarah T. Arron Wai-Ping Fung-Leung Ernesto Munoz Xuejun Liu Tina Bhutani Jeffrey North Wilson Liao 《The Journal of allergy and clinical immunology》2021,147(6):2370-2380
6.
7.
Structure detection of semiparametric structural equation models with Bayesian adaptive group lasso
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Xiang‐Nan Feng Guo‐Chang Wang Yi‐Fan Wang Xin‐Yuan Song 《Statistics in medicine》2015,34(9):1527-1547
Structural equation models (SEMs) are widely recognized as the most important statistical tool for assessing the interrelationships among latent variables. This study develops a Bayesian adaptive group least absolute shrinkage and selection operator procedure to perform simultaneous model selection and estimation for semiparametric SEMs, wherein the structural equation is formulated using the additive nonparametric functions of observed and latent variables. We propose the use of basis expansions to approximate the unknown functions. By introducing adaptive penalties to the groups of basis expansions, the nonlinear, linear, or non‐existent effects of observed and latent variables in the structural equation can be automatically detected. A simulation study demonstrates that the proposed method performs satisfactorily. This paper presents an application of revealing the observed and latent risk factors of diabetic kidney disease. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
8.
Ni Zhao Douglas A. Bell Arnab Maity Ana‐Maria Staicu Bonnie R. Joubert Stephanie J. London Michael C. Wu 《Genetic epidemiology》2015,39(2):53-64
New high throughput technologies are now enabling simultaneous epigenetic profiling of DNA methylation at hundreds of thousands of CpGs across the genome. A problem of considerable practical interest is identification of large scale, global changes in methylation that are associated with environmental variables, clinical outcomes, or other experimental conditions. However, there has been little statistical research on methods for global methylation analysis using technologies with individual CpG resolution. To address this critical gap in the literature, we develop a new strategy for global analysis of methylation profiles using a functional regression approach wherein we approximate either the density or the cumulative distribution function (CDF) of the methylation values for each individual using B‐spline basis functions. The spline coefficients for each individual are allowed to summarize the individual's overall methylation profile. We then test for association between the overall distribution and a continuous or dichotomous outcome variable using a variance component score test that naturally accommodates the correlation between spline coefficients. Simulations indicate that our proposed approach has desirable power while protecting type I error. The method was applied to detect methylation differences, both genome wide and at LINE1 elements, between the blood samples from rheumatoid arthritis patients and healthy controls and to detect the epigenetic changes of human hepatocarcinogenesis in the context of alcohol abuse and hepatitis C virus infection. A free implementation of our methods in the R language is available in the Global Analysis of Methylation Profiles (GAMP) package at http://research.fhcrc.org/wu/en.html . 相似文献
9.
Carolyn E. Schwartz Brian Stucky Carly S. Rivers Vanessa K. Noonan Joel A. Finkelstein 《Archives of physical medicine and rehabilitation》2018,99(8):1599-1608.e1
Objective
To investigate response shift effects in spinal cord injury (SCI) over 5 years postinjury.Design
Prospective cohort study observed at 1, 2, and 5 years post-SCI.Setting
Specialized SCI centers.Participants
Sample included 1125, 760, and 219 participants at 1, 2, and 5 years post-SCI (N = 2104). The study sample was 79% men; 39% were motor/sensory complete (mean age, 44.6±18.3y).Interventions
Not applicable.Main Outcome Measures
Patient-reported outcomes included the Medical Outcomes Study 36-Item Short-Form Health Survey version 2 and the Life Satisfaction-11 Questionnaire. Participant latent variable scores were adjusted for (1) potential attrition bias and (2) propensity scores reflecting risk of worse outcomes. The Oort structural equation modeling approach for detecting and accounting for response shift effects was used to test the hypothesis that people with SCI would undergo response shifts over follow-up.Results
The study data comprised the time after FIM scores, an objective measure of motor and cognitive function, had improved and stabilized. Three latent variables (Physical, Mental, and Symptoms) were modeled over time. The response shift model indicated uniform recalibration and reconceptualization response shift effects over time. When adjusted for these response shift effects, Physical showed small true change improvements at 2- and 5-year follow-up, despite FIM stability.Conclusions
We detected recalibration and reconceptualization response shift effects in 1- to 5-year follow-up of people with SCI. Despite stable motor and cognitive function, people with SCI are adapting to their condition. This adaptation reflects a progressive disconnection between symptoms and physical or mental health, and a real improvement in the Physical latent variable. 相似文献10.
模数转换器(Analog-to-Digital Converter,ADC)是片上集成系统的关键部件,通过对逐次逼近逻辑电路和三值逻辑原理的研究,提出了一种基于碳纳米场效应晶体管(Carbon Nanotube Field Effect Transistor,CNFET)的三值逐次逼近ADC设计方案。该方案首先控制三值电容阵列的底板电压,逐次逼近其模拟量值,产生由高位到低位的二值信号,然后由编码器将二值转换为三值信号,完成整个转换过程,最后实验证明了所设计的电路逻辑功能正确,并具有明显的高速、低功耗特性。 相似文献