| Contents |
| Accumulation of large amounts of measurements and simulation data give strong impulses to development of new data-driven approaches. One of the central challenges for the statistical analysis and data-driven long-time modelling methods in this area is posed by the intrinsically multiscale and multiphysics nature of the underlying phenomena.
One of the significant manifestations of this issue is that such approaches should be confronted with a problem of systematically missing information from unresolved or unmeasured scales. However, this missing information might be crucial for better understanding of the corse-grained dynamics. As demonstrated recently in general
mathematical context, such systematically missing data/information may induce non-stationarity of the resulting data-driven model for the observed/analyzed quantities and can lead to biased and distorted results when applying standard stationary data analysis methods to such problems. In this talk some new theoretical results for the case of spatio-temporal Markov process subject to impact of resolved and systematically-missing external impacts will be presented.
Limitations of standard data-analysis tools from machine learning (e.g., artificial neuronal networks and support vector machines) in this generic setting will be illustrated on a toy model system and application of the new framework to analysis
and understanding of satellite ice measurement data will be demonstrated. |
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