Rodrigo Iza-Teran

Rodrigo Iza-Teran, Jochen Garcke

We propose a new data analysis approach for the efficient post-processing of bundles of finite element data from numerical simulations. The approach is based on the mathematical principles of symmetry. We consider the case where simulations of an industrial product are contained in the space of surface meshes embedded in R^3. Furthermore, we assume that distance preserving transformations exist, albeit unknown, which map simulation to simulation. In this setting, a discrete Laplace-Beltrami operator can be constructed on the mesh, which is invariant to isometric transformations and therefore valid for all simulations. The eigenfunctions of such an operator are used as a common basis for all (isometric) simulations. One can use the projection coefficients instead of the full simulations for further analysis. To extend the idea of invariance, we employ a discrete Fokker-Planck operator, that in the continuous limit converges to an operator invariant to a nonlinear transformation, and use its eigendecomposition accordingly. The data analysis approach is applied to time-dependent datasets from numerical car crash simulations. One observes that only a few spectral coefficients are necessary to describe the data variability, and low dimensional structures are obtained. The eigenvectors are seen to recover different independent variation modes such as translation, rotation, or global and local deformations. An effective analysis of the data from bundles of numerical simulations is made possible, in particular an analysis for many simulations in time.

Sara Hahner, Rodrigo Iza-Teran, Jochen Garcke

For sequences of complex 3D shapes in time we present a general approach to detect patterns for their analysis and to predict the deformation by making use of structural components of the complex shape. We incorporate long short-term memory (LSTM) layers into an autoencoder to create low dimensional representations that allow the detection of patterns in the data and additionally detect the temporal dynamics in the deformation behavior. This is achieved with two decoders, one for reconstruction and one for prediction of future time steps of the sequence. In a preprocessing step the components of the studied object are converted to oriented bounding boxes which capture the impact of plastic deformation and allow reducing the dimensionality of the data describing the structure. The architecture is tested on the results of 196 car crash simulations of a model with 133 different components, where material properties are varied. In the latent representation we can detect patterns in the plastic deformation for the different components. The predicted bounding boxes give an estimate of the final simulation result and their quality is improved in comparison to different baselines.

Skylar Sible, Rodrigo Iza-Teran, Jochen Garcke et al.

Modern product design in the engineering domain is increasingly driven by computational analysis including finite-element based simulation, computational optimization, and modern data analysis techniques such as machine learning. To apply these methods, suitable data representations for components under development as well as for related design criteria have to be found. While a component's geometry is typically represented by a polygon surface mesh, it is often not clear how to parametrize critical design properties in order to enable efficient computational analysis. In the present work, we propose a novel methodology to obtain a parameterization of a component's plastic deformation behavior under stress, which is an important design criterion in many application domains, for example, when optimizing the crash behavior in the automotive context. Existing parameterizations limit computational analysis to relatively simple deformations and typically require extensive input by an expert, making the design process time intensive and costly. Hence, we propose a way to derive a compact descriptor of deformation behavior that is based on spectral mesh processing and enables a low-dimensional representation of also complex deformations.We demonstrate the descriptor's ability to represent relevant deformation behavior by applying it in a nearest-neighbor search to identify similar simulation results in a filtering task. The proposed descriptor provides a novel approach to the parametrization of geometric deformation behavior and enables the use of state-of-the-art data analysis techniques such as machine learning to engineering tasks concerned with plastic deformation behavior.