辛算法的分类与发展
wf(2021)
Abstract
辛算法作为研究哈密顿系统长期定性演化的最佳积分工具,自问世以来就受到了很大的关注.通过对哈密顿函数的截断误差分析,可以从不同角度构造出较高精度的辛算法,也可以通过引入正规化技术实现自动调整积分步长和改善数值稳定性.从辛算法的表现形式可以将它分为显式和隐式两种.当哈密顿系统能够分解为几个可积部分且每部分的解能用时间显函数来表示时,可以构造显式算法.显式算法有非力梯度显式辛算法、力梯度辛算法、辛校正、类高阶辛算法四种.当哈密顿系统变量不能分离时,适合应用隐式辛算法和扩充相空间对称算法求解.分别对这些算法的构造方法及其适用的物理模型进行归纳对比,分析了各种辛算法的优劣性和发展趋势,对如何选择辛算法高效高精度地解决实际问题提供了一定的理论和数值计算依据.
More求助PDF
上传PDF
View via Publisher
AI Read Science
AI Summary
AI Summary is the key point extracted automatically understanding the full text of the paper, including the background, methods, results, conclusions, icons and other key content, so that you can get the outline of the paper at a glance.
Example
Background
Key content
Introduction
Methods
Results
Related work
Fund
Key content
- Pretraining has recently greatly promoted the development of natural language processing (NLP)
- We show that M6 outperforms the baselines in multimodal downstream tasks, and the large M6 with 10 parameters can reach a better performance
- We propose a method called M6 that is able to process information of multiple modalities and perform both single-modal and cross-modal understanding and generation
- The model is scaled to large model with 10 billion parameters with sophisticated deployment, and the 10 -parameter M6-large is the largest pretrained model in Chinese
- Experimental results show that our proposed M6 outperforms the baseline in a number of downstream tasks concerning both single modality and multiple modalities We will continue the pretraining of extremely large models by increasing data to explore the limit of its performance
Upload PDF to Generate Summary
Must-Reading Tree
Example

Generate MRT to find the research sequence of this paper
Data Disclaimer
The page data are from open Internet sources, cooperative publishers and automatic analysis results through AI technology. We do not make any commitments and guarantees for the validity, accuracy, correctness, reliability, completeness and timeliness of the page data. If you have any questions, please contact us by email: report@aminer.cn
Chat Paper
Summary is being generated by the instructions you defined