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We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The solution is found as a multivariate nonlinear regression problem using the alternating conditional expectation algorithm. The procedure is successfully applied to data, obtained by simulation of the Swift-Hohenberg equation. There are no restrictions on the dimensionality of the investigated system, allowing for the analysis of high-dimensional chaotic as well as transient dynamics. The demands on the experimental data are discussed as well as the sensitivity of the method towards noise.
Voss et al. (Sun,) studied this question.