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Analysis of Crash Simulation Data using Spectral Embedding with Histogram Distances

Finite Element simulation of crash tests in the car industry generates huge amounts of high-dimensional numerical data. Methods from Machine Learning, especially from Dimensionality Reduction, can assist in analyzing and evaluating this data efficiently. Here we present a method that performs a two step dimensionality reduction in a novel manner: First the simulation data is represented as (normalized) histograms, then embedded into a low dimensional space using histogram distances and the nonlinear method of Spectral Embedding/Diffusion Maps, thus enabling a much easier data analysis. In particular, this method solves the problem of comparing simulation data with small changes in the Finite Element grids due to variations of geometry or unequally fine grid structures.