Robust Low-Rank Discovery of Data-Driven Partial Differential Equations

作者: Jun Li , Gan Sun , Guoshuai Zhao , Li-wei H. Lehman

DOI: 10.1609/AAAI.V34I01.5420

关键词: Partial derivativePartial differential equationCanonical modelAlgorithmParametric statisticsNoise (video)Rank (linear algebra)Data-drivenComputer science

摘要: … partial derivative terms of the governing PDEs that most accurately represent partial derivative data Ut of the collected data U. … ear and partial derivative terms of the governing PDEs that …

参考文章(24)
M. I. Jordan, T. M. Mitchell, Machine learning: Trends, perspectives, and prospects. Science. ,vol. 349, pp. 255- 260 ,(2015) , 10.1126/SCIENCE.AAA8415
Alfred M. Bruckstein, David L. Donoho, Michael Elad, From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images Siam Review. ,vol. 51, pp. 34- 81 ,(2009) , 10.1137/060657704
E. Elhamifar, R. Vidal, Sparse Subspace Clustering: Algorithm, Theory, and Applications IEEE Transactions on Pattern Analysis and Machine Intelligence. ,vol. 35, pp. 2765- 2781 ,(2013) , 10.1109/TPAMI.2013.57
Guangcan Liu, Zhouchen Lin, Shuicheng Yan, Ju Sun, Yong Yu, Yi Ma, Robust Recovery of Subspace Structures by Low-Rank Representation IEEE Transactions on Pattern Analysis and Machine Intelligence. ,vol. 35, pp. 171- 184 ,(2013) , 10.1109/TPAMI.2012.88
Amir Beck, Marc Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems Siam Journal on Imaging Sciences. ,vol. 2, pp. 183- 202 ,(2009) , 10.1137/080716542
Ran He, Tieniu Tan, Liang Wang, Robust Recovery of Corrupted Low-RankMatrix by Implicit Regularizers IEEE Transactions on Pattern Analysis and Machine Intelligence. ,vol. 36, pp. 770- 783 ,(2014) , 10.1109/TPAMI.2013.188
Jian-Feng Cai, Emmanuel J. Candès, Zuowei Shen, A Singular Value Thresholding Algorithm for Matrix Completion SIAM Journal on Optimization. ,vol. 20, pp. 1956- 1982 ,(2010) , 10.1137/080738970
Bruno A. Olshausen, David J. Field, Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1 ? Vision Research. ,vol. 37, pp. 3311- 3325 ,(1997) , 10.1016/S0042-6989(97)00169-7
Patrik O. Hoyer, Non-negative Matrix Factorization with Sparseness Constraints Journal of Machine Learning Research. ,vol. 5, pp. 1457- 1469 ,(2004) , 10.5555/1005332.1044709
Emmanuel J. Candès, Xiaodong Li, Yi Ma, John Wright, Robust principal component analysis? Journal of the ACM. ,vol. 58, pp. 1- 37 ,(2011) , 10.1145/1970392.1970395