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相关概念视频

Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

241
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
241
Reducing Line Loss01:18

Reducing Line Loss

173
In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss...
173
Downsampling01:20

Downsampling

188
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
188
Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

234
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
234
Deconvolution01:20

Deconvolution

190
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...
190
Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

88
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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相关实验视频

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Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
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通过多分辨率优化离散损失的自动差异化进行流量重建.

Petr Karnakov1, Sergey Litvinov1,2, Petros Koumoutsakos3

  • 1Computational Science and Engineering Laboratory, Harvard John A. Paulson School of Engineering and Applied Sciences, 29 Oxford St, Cambridge, MA, 02138, USA.

The European physical journal. E, Soft matter
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概括

我们开发了多分辨率优化一个DIScrete损失 (mODIL),一个快速的计算方法来解决流体力学反向问题. 这种强大的技术与物理信息神经网络 (PINNs) 相比,显著降低了计算成本.

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相关实验视频

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科学领域:

  • 计算流体动力学 计算流体动力学
  • 反向问题是反向的问题.
  • 优化方法优化方法.

背景情况:

  • 流体力学的反向问题对于理解和预测流体行为至关重要.
  • 解决这些问题的现有方法可能在计算上昂贵,并且容易产生局部最小值.
  • 优化分离损失 (ODIL) 框架为反向问题提供了确定性方法.

研究的目的:

  • 提出一种强大且加速的计算方法,用于解决流体力学中的反向问题.
  • 为了提高基于梯度的优化对基于网格的参数的效率和稳定性.
  • 与物理信息神经网络 (PINNs) 等现有方法相比,降低计算成本.

主要方法:

  • 引入多网格分解技术以加速基于梯度的优化.
  • 将多网格技术集成到优化不同损失 (ODIL) 框架中,创建多分辨率的ODIL (mODIL).
  • 在mODIL框架内利用自动区分来有效计算梯度.
  • 关于各种问题的演示:汉堡方程,导热推断和从唤醒速度的3D身体形状重建.

主要成果:

  • mODIL通过一个数量级加速了原来的ODIL框架.
  • 在优化过程中,mODIL 证明了更好的局部最小值避免.
  • 对比研究表明mODIL在基准问题上的计算成本比PINNs低3-5个数量级.
  • 成功应用于各种反向和流量重建任务,包括复杂的3D场景.

结论:

  • mODIL是一种非常强大,快速和一致的方法,用于解决流体力学的反向问题.
  • 开发的技术在PINNs等既定方法上提供了显著的计算优势.
  • 通过自动区分和改进的优化性能,mODIL促进了更容易的实现.