Julia Reuter

Julia Reuter, Fabricio Olivetti de Franca

Symbolic regression (SR) is a class of methods that systematically explore the space of mathematical functions to discover models that accurately capture the underlying relationships in a dataset. Despite recent advances in the field, a lack of support for uncertainty quantification (UQ) limits its adoption in real-world decision processes. In regression analysis, UQ provides important information about the model reliability, which can both help to avoid overfitting by accounting for uncertainty in the data, and provide insights for decision-making. This survey is the first to clearly address this issue, with the objective of introducing essential UQ concepts and reviewing the current literature on UQ in SR, which can be broadly organized into three research directions: frequentist, Bayesian, and model selection. Despite its importance, UQ in SR is still underexplored, which motivates further research into reliable UQ methods for SR.

Pravin Pandey, Julia Reuter, Christoph Steup et al.

This paper shows how a Graph Neural Network (GNN) can be used to learn an Inverse Kinematics (IK) based on an automatically generated dataset. The generated Inverse Kinematics is generalized to a family of manipulators with the same Degree of Freedom (DOF), but varying link length configurations. The results indicate a position error of less than 1.0 cm for 3 DOF and 4.5 cm for 5 DOF, and orientation error of 2$^\circ$ for 3 DOF and 8.2$^\circ$ for 6 DOF, which allows the deployment to certain real world-problems. However, out-of-domain errors and lack of extrapolation can be observed in the resulting GNN. An extensive analysis of these errors indicates potential for enhancement in the future. Consequently, the generated GNNs are tailored to be used in future work as an inductive bias to generate analytical equations through symbolic regression.