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Explainable Machine Learning for Scientific Insights and Discoveries
Ribana Roscher, Bastian Bohn, Marco F. Duarte +1
Machine learning methods have been remarkably successful for a wide range of application areas in the extraction of essential information from data. An exciting and relatively rece…
A Geometrical Method for Low-Dimensional Representations of Simulations
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 pr…
Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems
Laura von Rueden, Sebastian Mayer, Katharina Beckh +11
Despite its great success, machine learning can have its limits when dealing with insufficient training data. A potential solution is the additional integration of prior knowledge…
Simplex Stochastic Collocation for Piecewise Smooth Functions with Kinks
Barbara Fuchs, Jochen Garcke
Most approximation methods in high dimensions exploit smoothness of the function being approximated. These methods provide poor convergence results for non-smooth functions with ki…