在减少顺序建模中应用和比较几个自适应采样算法
Xirui Liu1, Zhiyong Wang1, Hongjun Ji2
1School of Mathematical Sciences, University of Electronic Science and Technology of China, 611731, Sichuan, China.
Heliyon
|August 22, 2024
概括
通过有效地探索复杂的参数空间,自适应采样算法显著改善了减少顺序建模 (ROM). 这些方法的性能优于标准策略,特别是在分歧和振荡的区域,提高了工程应用的模型准确性.
科学领域:
- 计算科学与工程 计算科学与工程
- 数字分析 数字分析
- 模型订单减少 (MOR)
背景情况:
- 模型顺序减少 (MOR) 对于模拟科学和工程中的复杂系统至关重要,包括核反应堆分析和流体力学.
- 减少订单模型 (ROM) 的有效性取决于离线阶段的基础函数选择,这在关键上取决于参数空间采样.
- 传统的采样策略经常与复杂的参数空间作斗争,在MOR.中构成重大挑战.
研究的目的:
- 在模型顺序减少的背景下,系统地评估和比较三个普遍的自适应采样算法的性能.
- 调查伪梯度采样,适应性稀疏网格采样和适应性训练集扩展用于MOR的应用和有效性.
- 为了证明这些适应性采样技术在现实世界工程问题中的实际实用性,例如核反应堆核心模拟.
主要方法:
- 专注于三个自适应采样算法:伪梯度采样,自适应稀疏网格采样和自适应训练集扩展.
- 系统性绩效评估和与标准采样策略进行比较.
- 在各种场景中应用和验证,包括核反应堆核心和对流问题.
主要成果:
- 与标准方法相比,自适应采样算法在捕获参数空间的分离和振荡区域方面表现出卓越的性能.
- 伪梯度采样对于小规模的MOR问题是有效的.
- 适应性稀疏网格采样和适应性培训集扩展非常适合在MOR.中面临的大规模采样挑战.
结论:
- 适应性采样算法在构建有效的减少订单模型 (ROM) 中取得了重大进展.
- 这些算法提高了采样效率和准确性,特别是在复杂和具有挑战性的参数空间中.
- 验证的应用证实了适应性采样在关键工程领域 (如核反应堆分析) 的实际价值.
相关概念视频
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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01:20Downsampling
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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...
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
141
01:22Upsampling
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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
216
01:15Sampling Theorem
315
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
315
01:18Aliasing
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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
124
01:11Sampling Continuous Time Signal
222
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
In the...
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