Automatic differentiation approach for solving one-dimensional flow and heat transfer problems

Niu, Yuhang; He, Yanan; Xiang, Fengrui; Zhang, Jing; Wu, Yingwei; Tian, Wenxi; Su, G.H.; Qiu, Suizheng

doi:10.1016/j.anucene.2021.108361

Cited by 16 publications

(2 citation statements)

References 20 publications

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“…For constructing matrix

{\hat {\bm C}_i}

, the gradient of

{Z_i}

needs to be estimated. There are several techniques can be used, such as linear regression, 38 surface method, 44 and automatic differentiation 45 …”

Section: Review Of Pcasmentioning

confidence: 99%

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High dimensional reliability analysis based on combinations of adaptive Kriging and dimension reduction technique

Xiao

Zhan

2022

Quality & Reliability Eng

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High dimensional reliability analysis is unavoidable if a structural system involving stochastic process because Karhunen–Loève (K‐L) expansion is commonly used. Reliability analysis for structural systems with computationally intensive numerical models and high dimensions is challenging. In this study, an effective high dimensional reliability analysis method is proposed based on principal components and active subspace (PCAS) and active Kriging, and is termed as PCAS‐AK. The proposed method can address two shortcomings existing in PCAS: the latter select training samples randomly and cannot deal with parallel processing. The proposed method, however, selects training samples adaptively, subsequently, the training samples that have high contribution to probability of failure are selected, which can improve computational efficiency. To reduce overall computational time and allow parallelization, K‐weighted‐means combined with learning function are used to select multiple samples at each iteration. After the dimension reduction of both input and output spaces, the samples selected by adaptive method are used to construct Kriging model in the latent low‐dimensional space. Three examples are used to demonstrate the applicability and accuracy of the proposed method. Results show that the proposed method can deal with parallel processing and is, generally, more effective than PCAS for high dimensional reliability problems.

show abstract

“…For constructing matrix

{\hat {\bm C}_i}

, the gradient of

{Z_i}

needs to be estimated. There are several techniques can be used, such as linear regression, 38 surface method, 44 and automatic differentiation 45 …”

Section: Review Of Pcasmentioning

confidence: 99%

“…There are several techniques can be used, such as linear regression, 38 surface method, 44 and automatic differentiation. 45 The advantages of using AS are as follows. First, fewer variables are used to represent the model output, that is, 𝐺 𝑖 (𝜼) is used to replace of 𝑓 𝑖 (𝑿).…”

Section: Input Dimension Reduction Using Asmentioning

confidence: 99%

High dimensional reliability analysis based on combinations of adaptive Kriging and dimension reduction technique

Xiao

Zhan

2022

Quality & Reliability Eng

View full text Add to dashboard Cite

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A new method to simulate dispersion plate-type fuel assembly in a multi-physics coupled way

Xiang

Niu

et al. 2022

Annals of Nuclear Energy

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A modified JFNK method for solving the fundamental eigenmode in k-eigenvalue problem

Liu

et al. 2022

Annals of Nuclear Energy

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Automatic differentiation approach for solving one-dimensional flow and heat transfer problems

Cited by 16 publications

References 20 publications

High dimensional reliability analysis based on combinations of adaptive Kriging and dimension reduction technique

High dimensional reliability analysis based on combinations of adaptive Kriging and dimension reduction technique

A new method to simulate dispersion plate-type fuel assembly in a multi-physics coupled way

A modified JFNK method for solving the fundamental eigenmode in k-eigenvalue problem

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