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相关概念视频

Uncertainty: Overview00:59

Uncertainty: Overview

564
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
564
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

699
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
699
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

56
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...
56
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

529
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
529

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相关实验视频

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在计算人类头部模型中的数据驱动的不确定性量化.

Kshitiz Upadhyay1,2, Dimitris G Giovanis3, Ahmed Alshareef4

  • 1Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD 21218, USA.

Computer methods in applied mechanics and engineering
|November 23, 2023
PubMed
概括
此摘要是机器生成的。

计算头模型的不确定性量化 (UQ) 对于预测创伤性脑损伤至关重要. 一个新的数据驱动框架降低了计算成本,揭示了大脑应变不确定性的空间变化.

关键词:
高斯过程回归的高斯过程回归.格拉斯曼的扩散地图.头部伤害模型的模型替代模型的替代模型创伤性脑损伤 (TBI) 是一种创伤性脑损伤.不确定性量化不确定性的量化.

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科学领域:

  • 生物力学 生物力学
  • 计算建模计算建模
  • 不确定性量化不确定性的量化.

背景情况:

  • 计算头部模型对于预测创伤性脑损伤 (TBI) 至关重要.
  • 模型参数 (几何,材料属性,边界条件) 的重大不确定性挑战了预测可靠性.
  • 生物忠实头部模型的高计算成本限制了传统的不确定性量化 (UQ) 方法.

研究的目的:

  • 开发和验证一个新的两阶段,数据驱动的多重学习框架,用于计算头模型的UQ.
  • 在高维度生物忠实模拟中解决UQ的计算成本.
  • 为了量化模拟大脑应变场中的不确定性,由于材料性质的变化.

主要方法:

  • 一个两阶段的框架,将多元学习与替代模型结合起来.
  • 第一个阶段:数据驱动生成输入随机向量实现,使用内核密度估计和扩散图.
  • 第二阶段:训练具有非线性维度缩小的替代模型 (格拉斯曼的扩散图,高斯的过程回归,几何波),以实现高效的输入输出映射.

主要成果:

  • 拟议的框架大大降低了计算成本,同时在近似计算头模型响应方面保持了高准确性.
  • 使用替代模型的蒙特卡洛模拟有效地传播不确定性.
  • UQ分析揭示了模型不确定性的显著空间变化以及脑损伤预测变量之间的差异.

结论:

  • 数据驱动的多元学习框架为UQ在复杂的计算头模型中提供了高效和准确的方法.
  • 这种方法通过表征模拟大脑反应的不确定性来提高TBI预测的可靠性.
  • 这些发现强调了考虑不确定性的空间变化对于准确的TBI风险评估的重要性.