Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 115, Issue 43, Pages E9994-E10002Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1802987115
Keywords
prediction; nonlinear dynamics; time series; high-dimensional data; short-term data
Categories
Funding
- National Key R & D Program of China [2017YFA0505500, 2018YFC0116600]
- Chinese Academy of Sciences [XDB13040700]
- Japan Society for the Promotion of Science [15H05707]
- WPI, Ministry of Education, Culture, Sports, Science and Technology, Japan
- National Natural Science Foundation of China [91530320, 11322111, 11771010, 61773125]
- Science and Technology Commission of Shanghai Municipality [18DZ1201000]
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Future state prediction for nonlinear dynamical systems is a challenging task, particularly when only a few time series samples for high-dimensional variables are available from real-world systems. In this work, we propose a model-free framework, named randomly distributed embedding (RDE), to achieve accurate future state prediction based on short-term high-dimensional data. Specifically, from the observed data of high-dimensional variables, the RDE framework randomly generates a sufficient number of low-dimensional nondelay embeddings and maps each of them to a delay embedding, which is constructed from the data of a to be predicted target variable. Any of these mappings can perform as a low-dimensional weak predictor for future state prediction, and all of such mappings generate a distribution of predicted future states. This distribution actually patches all pieces of association information from various embeddings unbiasedly or biasedly into the whole dynamics of the target variable, which after operated by appropriate estimation strategies, creates a stronger predictor for achieving prediction in a more reliable and robust form. Through applying the RDE framework to data from both representative models and real-world systems, we reveal that a high-dimension feature is no longer an obstacle but a source of information crucial to accurate prediction for short-term data, even under noise deterioration.
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