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相关概念视频

Efficiency of The Carnot Cycle01:16

Efficiency of The Carnot Cycle

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The hypothetical Carnot cycle consists of an ideal gas subjected to two isothermal and two adiabatic processes. Since the internal energy of an ideal gas depends only on its temperature, which is the same before and after the completion of the Carnot cycle, there is no change in its internal energy. Hence, using the first law of thermodynamics, the total heat exchanged by the ideal gas equals the total work done. Thus, we can quantify the efficiency of the Carnot cycle via the heat exchanged...
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Solving Problems in Physics02:32

Solving Problems in Physics

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Problem-solving is the ability to apply general physical principles to specific situations, usually expressed by equations. It is an essential skill in physics, and can also be useful for applying physics in everyday life as well. Analytical skills and problem-solving abilities can be applied to new situations, compared to a list of facts, which can never be extensive enough to include every possible circumstance. To solve physics problems, a certain amount of creativity and insight is...
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Conduction, Convection and Radiation: Problem Solving01:20

Conduction, Convection and Radiation: Problem Solving

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There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting characteristics, but all three have two things in common: they transfer heat solely because of a temperature difference; and the greater the temperature difference, the faster the heat transfer.
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could...
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Energy Conservation and Bernoulli's Equation01:16

Energy Conservation and Bernoulli's Equation

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Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
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The Carnot Cycle01:30

The Carnot Cycle

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Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the efficiency of the reversal, that is, maximize the work retrieved from heat. If the efficiency of a heat engine were 100%, it would imply reversing the process completely without introducing any other effect. Thus, it would violate the second law of thermodynamics.
What could be the theoretical limit to the efficiency of a heat engine? The...
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Mechanisms of Heat Transfer I01:14

Mechanisms of Heat Transfer I

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Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature difference, heat transfer occurs. It may occur rapidly, such as through a cooking pan, or slowly, such as through the walls of a picnic ice box. So many processes involve heat transfer that it is hard to imagine a situation where no heat transfer occurs. Yet, every heat transfer takes place by only three methods: conduction, convection, and radiation.
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Knowledge Based Cloud FE Simulation of Sheet Metal Forming Processes
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如何转移你的知识学习隐藏的物理学的知识.

Lu Zhang1, Huaiqian You1, Tian Gao2

  • 1Department of Mathematics, Lehigh University, Bethlehem, PA, USA.

Computer methods in applied mechanics and engineering
|January 31, 2024
PubMed
概括

本研究引入了一种新的超学习方法,用于神经操作员在不同的材料参数中高效地学习部分微分方程 (PDEs) 的解决方案. 该方法增强了复杂物理系统的知识传输,提高了材料建模中的数据效率.

关键词:
数据驱动的物理建模超级学习 (Meta-Learning) 是一种学习方式.神经运营者 神经运营者运营商回归神经网络 运营商回归神经网络科学机器学习科学机器学习转移学习 转移学习

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科学领域:

  • 计算物理学的计算物理.
  • 机器学习 机器学习
  • 材料科学是一种材料科学.

背景情况:

  • 基于梯度的元学习通常用于图像分类.
  • 神经运算机正在出现,可以从数据中学习复杂的物理系统,作为PDE的替代模型.
  • 由于实验成本和局限性,材料建模在数据采集方面面临挑战.

研究的目的:

  • 为神经运算符开发一种新的元学习方法,以实现知识转移,以解决具有变化的参数字段的部分微分方程 (PDEs).
  • 提高材料科学中PDEs的学习解决方案运营商的抽样效率.
  • 为多个PDE解决任务创建一个普遍适用的解决方案操作员.

主要方法:

  • 为神经操作员提出了一个元学习框架,以便在具有不同参数字段的PDEs之间传输知识.
  • 从理论上证明,参数场可以在神经操作员模型的第一层中被捕获.
  • 将方法应用于基于PDE的数据集和现实世界的材料建模问题.

主要成果:

  • 拟议的元学习方法使解决方案运营商知识在不同参数领域的有效转移成为可能.
  • 参数场信息有效地编码在神经操作员的初始层中.
  • 该方法成功地处理复杂的非线性物理响应学习任务.

结论:

  • 这种新的元学习方法显著提高了未见材料标本的采样效率.
  • 这种方法为多个PDE解决任务提供了一个可证明的通用解决方案操作员.
  • 这种方法在材料建模中对复杂的物理响应学习有效,解决了数据采集的挑战.