机器学习 K-Means 集群交互可分离密度拟合算法,用于准确和高效的立方缩放精确交换加随机相近似在平面波内
Zhenlin Zhang1, Xilin Yin1, Wei Hu1
1Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Journal of chemical theory and computation
|February 16, 2024
概括
我们开发了一种高效的机器学习方法,用于使用精确交换加随机相近似 (EXX+RPA) 进行电子结构计算. 这种方法显著加速计算,使分子和固体系统的表征更快.
科学领域:
- 计算化学和材料科学计算化学和材料科学
- 量子力学模拟的量子力学模拟
- 电子结构理论 电子结构理论
背景情况:
- 精确交换加随机相近似 (EXX+RPA) 方法对于分子和固体的电子结构表征至关重要.
- 传统的EXX+RPA实现面临着计算方面的挑战,特别是平面波基集和互插可分离密度拟合 (ISDF) 算法.
- 在ISDF中使用的QRCP算法,对插值点选择具有很高的前因子,限制了计算效率.
研究的目的:
- 开发使用平面波的EXX+RPA计算的准确和高效实现.
- 通过引入增强的机器学习K-means方法来缓解ISDF中的计算瓶,用于插值点选择.
- 改进整体计算扩展和加速EXX+RPA计算,包括GPU优化.
主要方法:
- 实现了EXX+RPA计算,在平面波基集合内采用立方缩放方法.
- 集成了互极分离密度拟合 (ISDF) 算法.
- 引入了一种机器学习的K-means方法,具有新的"SSM+"权重函数,用于改进插值点的选择,将立方缩放QRCP算法替换为准方程缩放的替代方案.
- 使用 MATLAB 集成的 GPU 工具包优化了 GPU 加速.
主要成果:
- 介电函数 (χ0) 的计算缩小缩放从3.80到2.13,整体EXX缩放从2.74到2.10.
- 实现了高达35倍的GPU加速加速.
- 证明了显著的CPU时间减少:K-means将Si128的计算时间从22小时 (标准) 减少到800秒 (100×改进),QRCP插曲点计算时间从1小时到1分钟 (55×速度增加).
- 成功计算了H2解离曲线和C18多态几何.
结论:
- 开发的机器学习增强的EXX+RPA方法为电子结构计算提供了计算效率高,准确的方法.
- 准方程缩放和GPU加速提供了相当大的加速度,使复杂的计算更加可行.
- 这种改进的方法使得研究更大,更复杂的分子和固体系统成为可能.
相关概念视频
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
502
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...
502
Extraction: Partition and Distribution Coefficients
2.4K
The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...
For extracting a solute from an aqueous phase into an...
2.4K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
54
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
54
Cluster Sampling Method
11.9K
Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
11.9K
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
69
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
69
Reduced Mass Coordinates: Isolated Two-body Problem
1.3K
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
1.3K


