UC Merced

We study two methods to analyze spatio-temporal data. To describe data, we use principal component analysis. To predict data, we use dynamic mode decomposition. We compute numerical solutions of the complex Ginzburg-Landau equation and we use that numerical solution as data. Using principal component analysis we identify a low-dimensional subspace spanned by only 3 principal components. Using these 3 principal components we can reconstruct the original data matrix with approximately 2% error, and construct out-of-sample data with less than 3% error. Using dynamic mode decomposition we are able to predict the temporal evolution of out-of-sample data as far as 500 time steps into the future with less than 5% error. The combination of these two techniques provides robust and reliable methods to analyze complex data sets.