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相关概念视频

Fast Fourier Transform01:10

Fast Fourier Transform

290
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
290
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

45
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...
45

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相关实验视频

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在使用人工智能硬件和GPU的电子结构计算中,有效的反重叠矩阵的混合精度矩阵因子化.

Adela Habib1, Joshua Finkelstein1, Anders M N Niklasson1

  • 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States.

Journal of chemical theory and computation
|August 13, 2024
PubMed
概括

本研究介绍了一种混合精度算法,用于使用Nvidia Tensor核心对逆重叠矩阵 (S^-1) 的密度矩阵分解. 该方法实现了电子结构计算的高性能,为复杂的模拟提供了可靠的方法.

科学领域:

  • 计算化学是一种计算化学.
  • 人工智能硬件加速 硬件加速

背景情况:

  • 深度神经网络计算越来越多地利用人工智能硬件进行高性能张量收缩.
  • 电子结构理论需要有效计算反重叠矩阵 (S^-1) 来解决矩阵自值问题.

研究的目的:

  • 开发一种混合精度算法,用于使用Nvidia Tensor核心对S^-1的密度矩阵分解.
  • 与传统的GPU实现相比,评估这种方法的性能和准确性.

主要方法:

  • 利用Nvidia Tensor核心以降低精度进行高性能张量收缩.
  • 开发一种混合精度的代精细化算法,用于S^-1分解 (ZZ^T = S^-1).
  • 实施一个强大的非参数停止标准,以降低精度的浮点运算.

主要成果:

  • 通过矩阵-矩阵乘法计算Z的Tensor核心的高性能证明.
  • 将混合精度方法与仅GPU的单双精度实现进行了比较.
  • 在降低精度下验证了非参数式停止标准的稳定性.

结论:

  • 混合精度代精细化算法为Tensor核心上的S^-1分解提供了高性能解决方案.

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  • 这种方法特别有利于量子力学分子动力学和几何优化,当有良好的初始猜测可用时.
  • 非参数停止标准确保可靠的计算,尽管潜在的精度限制.