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Prediction in Projection

Joshua Garland

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Date and time:Ìý

Thursday, October 22, 2015 - 2:00pm

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ECCR 257

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Prediction models constructed from state-space dynamics have a long and rich history, dating back to roulette and beyond.Ìý A major stumbling block in the application of these models in real-world situations is the need to reconstruct the dynamics from scalar time-series data - e.g., via delay-coordinate embedding.Ìý This procedure, which is the subject of a large and active body of literature, involves estimation of two free parameters: the dimension of the reconstruction space and the delay between the observations that make up the coordinates in that space.Ìý Estimating good values for these parameters is not trivial; it requires the proper mathematics, attention to data requirements, computational effort, and expert interpretation of the results of the calculations. This is a major challenge if one is interested in real-time forecasting, especially when the systems involved operate on fast time scales.

In this talk, I will show that the full effort of delay-coordinate embedding is not always necessary when one is building forecast models - and can indeed be overkill. Using synthetic time-series data generated from the Lorenz-96 atmospheric model, as well as experimental data, I will demonstrate that a two-dimensional reconstruction of scalar time-series data from a dynamical system allows one to generate accurate predictions of the future course of those dynamics - sometimes even more accurate than predictions created using an embedding.Ìý Since incomplete reconstructions do not preserve the topology of the full dynamics, this is interesting from a mathematical standpoint.Ìý It is also potentially useful in practice.Ìý This reduced-order forecasting strategy involves only one free parameter - good values for which, I will show, can be estimated ‘on the fly’.Ìý As such, it sidesteps much of the complexity of the embedding process - perhaps most importantly, the need for expert human interpretation - and thus could enable automated, real-time dynamics-based forecasting in practical applications.