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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Beams are structural elements commonly employed in engineering applications requiring different load-carrying capacities. The first step in analyzing a beam under a distributed load is to simplify the problem by dividing the load into smaller regions, which allows one to consider each region separately and calculate the magnitude of the equivalent resultant load acting on each portion of the beam. The magnitude of the equivalent resultant load for each region can be determined by calculating...
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Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
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相关实验视频

Updated: Jun 5, 2025

Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches
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一个推断驱动的网络架构,用于基于物理的深度学习.

Yong Wang1, Yanzhong Yao2, Zhiming Gao2

  • 1Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; Graduate School of China Academy of Engineering Physics, Beijing 100088, China; National Key Laboratory of Computational Physics, Beijing 100088, China.

Neural networks : the official journal of the International Neural Network Society
|December 10, 2024
PubMed
概括

基于物理学的神经网络 (PINNs) 难以进行顺序学习. 本研究介绍了一种推断驱动的网络架构,可以克服这些局限性,为大域的时间依赖PDE提供准确和连续的解决方案.

关键词:
深度学习是一种深度学习.进化方程式的演化方程式额外推算是指进行额外推算.基于物理学的神经网络.

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科学领域:

  • 计算科学 计算科学
  • 应用数学 应用数学 应用数学
  • 人工智能的人工智能

背景情况:

  • 当前的物理信息神经网络 (PINN) 方法在依赖时间的部分微分方程 (PDEs) 的顺序学习方面面临挑战.
  • 这些挑战包括单个网络的可重现性问题和多个网络的连续性/平滑性问题,以及计算成本的增加.
  • 现有的方法很难在广泛的时间域中有效地解决进化方程.

研究的目的:

  • 调查和利用PINNs对时间依赖的PDE的推断能力.
  • 开发一种新的神经网络架构,解决PINNs中当前顺序学习策略的局限性.
  • 通过使用单一网络,在很长的时间间隔内实现PDE的准确,连续和顺的解决方案.

主要方法:

  • 研究了PINNs对时间依赖的PDE的推断属性.
  • 开发了一个校正术语,将训练结果从子间隔推广到更大的间隔.
  • 引入了外推驱动的网络架构,通过外推控制函数将网络参数与时间变量合起来.
  • 采用单个神经网络,在多个子间隔内按时间顺序训练,尊重因果关系.

主要成果:

  • 以外推驱动的网络架构成功地继承了先前培训间隔的本地解决方案.
  • 在间隔节点保持严格的连续性和平滑性,匹配真正的解决方案.
  • 该方法有效地克服了传统PINNs在解决大时间域上的进化方程方面的困难.
  • 数值实验验证实了拟议方法的性能.

结论:

  • 推断驱动的网络架构为PINNs的顺序学习提供了一个强大的解决方案.
  • 这种方法提高了准确性,连续性和效率,在解决大领域的时间依赖的PDEs时.
  • 该方法尊重因果关系,并简化了处理复杂进化方程的过程.