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相关概念视频

Deconvolution01:20

Deconvolution

260
Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
260
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

416
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
416
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

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The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
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Two-Dimensional Force System01:20

Two-Dimensional Force System

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A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:
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Convolution Properties II01:17

Convolution Properties II

288
The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
288
Convolution Properties I01:20

Convolution Properties I

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Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
240

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深潜力模型:贝叶斯深度学习的基于ODE的过程卷曲.

Thomas Baldwin-McDonald1, Xinxing Shi1, Mingxin Shen1

  • 1Department of Computer Science, University of Manchester, Oxford Road, Manchester, M13 9PL UK.

Machine learning
|July 18, 2025
PubMed
概括
此摘要是机器生成的。

我们介绍了深潜力模型 (DLFM),这是一个用于建模非线性动态系统的新方法. 这种以物理学为基础的高斯过程模型有效量化不确定性,并捕捉复杂的时间序列动态.

关键词:
贝叶斯深度学习是贝叶斯的深度学习.斯过程是高斯过程.基于物理的机器学习.可能的机器学习.

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科学领域:

  • 机器学习 机器学习
  • 动态系统建模 动态系统建模
  • 不确定性定量化 不确定性定量化

背景情况:

  • 建模高度非线性动态系统与强大的不确定性量化是复杂的.
  • 现有的方法往往需要针对特定问题的设计.
  • 为了更广泛的适用性,需要一种域异的方法.

研究的目的:

  • 为非线性动态系统引入一个域不可知模型.
  • 开发一个深度高斯过程与物理学知情的内核.
  • 在复杂系统建模中实现可靠的不确定性量化.

主要方法:

  • 开发了深潜力力模型 (DLFM),一种深度高斯过程.
  • 从普通微分方程中获得的内置物理信息的内核.
  • 使用了两种配方:重量空间和变化诱导点.
  • 采用双倍随机变化推理用于模型近似.

主要成果:

  • DLFM有效地捕获高度非线性,多输出时间序列数据中的动态.
  • 在回归任务上实现了与非物理知情模型可比的性能.
  • 确定了诱导点对外推算能力的负面影响.

结论:

  • DLFM为模拟复杂的动态系统提供了一种强大的,域异的解决方案.
  • 基于物理的内核增强了模型捕捉系统动态和量化不确定性的能力.
  • 需要进一步的研究来优化外推性能.