arXiv subjects

Julia Reuter

Publications and source records attributed to Julia Reuter.

5 recordsLinked to original sources

arXiv2026

Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression

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.

cs.LG↗

arXiv2025

Drag modelling for flows through assemblies of spherical particles with machine learning: A comparison of approaches

Drag forces on particles in random assemblies can be accurately estimated through particle-resolved direct numerical simulations (PR-DNS). Despite its limited applicability to relatively small assemblies, data obtained from PR-DNS has been the driving force for the development of drag closures for much more affordable simulation frameworks, such as Eulerian-Lagrangian point particle methods. Recently, more effort has been invested in the development of deterministic drag models that account for the effect of the structure of the particle assembly. Current successful deterministic models are mainly black-box neural networks which: 1) Assume pairwise superposition of the neighbours' effect on the drag, and 2) Are trained on PR-DNS data for a wide range of particle concentrations and flow regimes. To alleviate the black-box nature of neural networks, we use genetic programming (GP) to develop interpretable models. In our previous research, this has been proven successful in the Stokes regime. In the current contribution, we extend the application of GP to higher particle Reynolds number regimes. This is done by training a graph neural network (GNN) on the PR-DNS data to learn the pairwise interactions among the particles that constitute the drag variation. The significance of the input features of the GNN is assessed via a feature permutation approach. Then, the estimated pairwise interactions as extracted from the GNN are fed to a GP algorithm, which searches for symbolic expressions that fit the input data. A comparison between the trained GNN model and the resulting symbolic expressions is presented, to assess whether the symbolic expression can capture the underlying patterns learnt by the GNN. The comparison demonstrates the potential of GP in finding relatively simple symbolic models. At the same time, the accuracy of the symbolic models slightly fall behind the GNN.

physics.comp-ph↗

arXiv2025

The Road to Learning Explainable Inverse Kinematic Models: Graph Neural Networks as Inductive Bias for Symbolic Regression

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.

cs.RO↗

arXiv2024

Shape Constraints in Symbolic Regression using Penalized Least Squares

We study the addition of shape constraints (SC) and their consideration during the parameter identification step of symbolic regression (SR). SC serve as a means to introduce prior knowledge about the shape of the otherwise unknown model function into SR. Unlike previous works that have explored SC in SR, we propose minimizing SC violations during parameter identification using gradient-based numerical optimization. We test three algorithm variants to evaluate their performance in identifying three symbolic expressions from synthetically generated data sets. This paper examines two benchmark scenarios: one with varying noise levels and another with reduced amounts of training data. The results indicate that incorporating SC into the expression search is particularly beneficial when data is scarce. Compared to using SC only in the selection process, our approach of minimizing violations during parameter identification shows a statistically significant benefit in some of our test cases, without being significantly worse in any instance.

cs.LG↗

arXiv2024

Unit-Aware Genetic Programming for the Development of Empirical Equations

When developing empirical equations, domain experts require these to be accurate and adhere to physical laws. Often, constants with unknown units need to be discovered alongside the equations. Traditional unit-aware genetic programming (GP) approaches cannot be used when unknown constants with undetermined units are included. This paper presents a method for dimensional analysis that propagates unknown units as ''jokers'' and returns the magnitude of unit violations. We propose three methods, namely evolutive culling, a repair mechanism, and a multi-objective approach, to integrate the dimensional analysis in the GP algorithm. Experiments on datasets with ground truth demonstrate comparable performance of evolutive culling and the multi-objective approach to a baseline without dimensional analysis. Extensive analysis of the results on datasets without ground truth reveals that the unit-aware algorithms make only low sacrifices in accuracy, while producing unit-adherent solutions. Overall, we presented a promising novel approach for developing unit-adherent empirical equations.

cs.LG↗