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相关概念视频

Second Derivatives of Implicit Functions01:29

Second Derivatives of Implicit Functions

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Elliptical arches are fundamental in architectural and structural engineering, offering aesthetic appeal and structural efficiency. The shape of an elliptical arch follows a constrained geometric relationship where the height and horizontal position are implicitly related. This means that the height y cannot be explicitly expressed as a function of the horizontal position x, necessitating implicit differentiation for slope and curvature analysis.The equation of an ellipse centered at the origin...
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Approximate Integration01:24

Approximate Integration

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In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
51
Implicit Differentiation01:25

Implicit Differentiation

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In classical mechanics, motion is often described through relationships between spatial coordinates and time. A car moving along a straight highway with constant acceleration serves as a simple case where velocity is an explicit function of time. This scenario results in a linear equation, enabling straightforward analysis using basic differentiation techniques.In contrast, a satellite in circular orbit follows a path defined by an implicit function. The position of the satellite is constrained...
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Implicit Memories01:24

Implicit Memories

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Implicit memories, also known as non-declarative memories, are long-term memories that function outside of conscious awareness. These memories influence behavior and skills without explicit knowledge. This type of memory is evident in tasks like playing tennis, snowboarding, and texting. Implicit memory has three subsystems: procedural memory, conditioning, and priming. This type of memory is essential in various activities, from everyday tasks to specialized skills.
One key aspect of implicit...
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Linearization and Approximation01:26

Linearization and Approximation

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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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Accuracy, limits, and approximation01:28

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Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
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通过隐式相互依赖模型对近似函数的多目标优化.

Ziying Yuan1, Neil Qiang Su1

  • 1Center for Theoretical and Computational Chemistry, Frontiers Science Center for New Organic Matter, State Key Laboratory of Advanced Chemical Power Sources, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Department of Chemistry, Nankai University, Tianjin 300071, China.

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概括
此摘要是机器生成的。

本研究介绍了EBI4MO,这是一个新的多目标优化框架,用于开发精确的密度函数理论 (DFT) 交换-相关性 (XC) 函数. EBI4MO确保了各种化学系统的平衡性能,优于传统方法.

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科学领域:

  • 计算化学的计算化学
  • 量子化学 是一个量子化学.
  • 材料科学 材料科学 材料科学

背景情况:

  • 准确的交换相关性 (XC) 函数对于密度函数理论 (DFT) 的预测能力至关重要.
  • 传统的XC功能优化通常使用单一目标或步骤方法,导致不同化学系统的性能不平衡.
  • 有需要的方法,可以同时优化XC函数的多个性能标准.

研究的目的:

  • 引入一个多目标优化框架,EBI4MO (多目标的明确隐含),用于XC函数的同时和一致的优化.
  • 为了使XC函数的开发能够在各种化学应用中具有平衡的性能.
  • 为了证明EBI4MO在优化混合XC函数和分散校正方面的有效性.

主要方法:

  • 开发了EBI4MO,这是一个使用隐性函数层次结构来对多个目标之间相互依赖的参数组进行配对的框架.
  • 应用EBI4MO以优化混合XC函数的参数,并进行分散校正.
  • 使用GMTKN55基准数据库进行优化,考虑两个目标:尽量减少整体预测错误,实现相对于B3LYP-D3的统一改进.

主要成果:

  • EBI4MO框架成功地优化了混合XC函数用分散校正.
  • 由此产生的函数在GMTKN55数据库的所有基准子集中显示出一致和平衡的性能.
  • 使用 EBI4MO 优化的功能性比使用传统单一目标或逐步优化方法开发的功能性更好.

结论:

  • EBI4MO是一个有效的和可泛化的框架,用于计算化学中的多目标优化.
  • 这种方法为开发具有改进和平衡预测能力的XC函数提供了一个新的策略.
  • EBI4MO提供了一种强大的方法来解决计算化学中更广泛的多目标优化挑战.