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Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action (-log[P]). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series s(tn);tn=t0+n Delta t and, using methods of nonlinear time series analysis, show how to produce a DE>1-dimensional time-delay embedding space in which the time series has no false neighbors as does the observed s(tn) time series. In that DE-dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on DE-dimensional input and producing DE-dimensional outputs.
Proxy-based reconstructions and modeling of Holocene spatiotemporal precipitation patterns for China and Mongolia have hitherto yielded contradictory results indicating that the basic mechanisms behind the East Asian Summer Monsoon and its interaction with the westerly jet stream remain poorly understood. We present quantitative reconstructions of Holocene precipitation derived from 101 fossil pollen records and analyse them with the help of a minimal empirical model. We show that the westerly jet-stream axis shifted gradually southward and became less tilted since the middle Holocene. This was tracked by the summer monsoon rain band resulting in an early-Holocene precipitation maximum over most of western China, a mid-Holocene maximum in north-central and northeastern China, and a late-Holocene maximum in southeastern China. Our results suggest that a correct simulation of the orientation and position of the westerly jet stream is crucial to the reliable prediction of precipitation patterns in China and Mongolia.