# Overview

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This workshop will focus on identification, characterization, and prediction of nonlinear dynamics from high dimensional time series data sets. It will combine the ideas from the first workshop on rigorous computation in infinite dimensions and the tools from the tutorial with analytic and topological approaches to data analysis in the context of explicit applications. The workshop will be centered around three related fundamental challenges that require foundational mathematical development:

- Dimension reduction. Modern data sets often have extremely high extrinsic dimension, but the information content is much lower dimensional. As an example consider complicated fluid flow. Using Navier-Stokes as a model makes an infinite dimensional problem. Modern numerical simulations and experimentally collected data can easily involve million dimensional approximations. However, for many problems of interest the dimension of the attractor is on the order of 100 or less.
- Phase space reconstruction from data. Typically only a subset of the relevant variables are observed. Therefore to capture the full dynamics requires some form of reconstruction of a model of phase space.
- Information extraction. Typically the information of interest involves identification of dynamic structures or the possibility of prediction of dynamic behavior. Given that the input data is noisy and that steps 1 and 2 involve processing the data, one needs robust techniques for extracting information.

Addressing these challenges requires both theory and computation, and validation involves successful applications to physical systems. With this in mind we invited a broad range of speakers. Theoretical approaches that will be represented include topological data analysis, diffusion operators, and Koopman operators. Computational talks will cover subjects such as high dimensional linear algebra, computational homology, high dimensional numerical simulations of nonlinear systems, and rigorous computational techniques. Finally, we invited speakers that are interested in specific applications involving high dimensional data sets including biochemistry, network dynamics, fluid mechanics, and dense granular material.