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RANK-MINIMIZING AND STRUCTURED MODEL INFERENCE
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AI
DOI：10.1137/23M1554308.png)
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摘要
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While extracting information from data with machine learning plays an increasingly important role, physical laws and other first principles continue to provide critical insights about systems and processes of interest in science and engineering. This work introduces a method that infers models from data with physical insights encoded in the form of structure and that minimizes the model order so that the training data are fitted well while redundant degrees of freedom without conditions and sufficient data to fix them are automatically eliminated. The models are formulated via solution matrices of specific instances of generalized Sylvester equations that enforce interpolation of the training data and relate the model order to the rank of the solution matrices. The proposed method numerically solves the Sylvester equations for minimal-rank solutions and so obtains models of low order. Numerical experiments demonstrate that the combination of structure preservation and rank minimization leads to accurate models with orders of magnitude fewer degrees of freedom than models of comparable prediction quality that are learned with structure preservation alone.
Keyword:
system identification
structured systems
transfer function data
nuclear-norm
rank-minimization problems
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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Structural and magnetic changes in Li substituted YBa2Cu3Oy determined by neutron powder diffraction measurements通过中子粉末衍射测量确定的Li取代YBa₂Cu₃Oy的结构和磁性变化
PREAI
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