Researcher profile

Martin Roelfs

Martin Roelfs contributes to research discovery and scholarly infrastructure.

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Published work

6 published item(s)

preprint2026arXiv

CAD-feature enhanced machine learning for manufacturing effort estimation on sheet metal bending parts

Graph-based machine learning has emerged as a promising approach for manufacturability analysis by learning directly from CAD models represented as Boundary Representations (B-reps), exploiting both surface geometry and topological connectivity. However, purely geometric representations often lack the process-specific semantics required for accurate manufacturability prediction: many manufacturing factors, such as surface roles or bend intent, are not explicitly encoded in shape alone and are difficult for data-driven models to infer reliably. We propose a hybrid approach that addresses this challenge by enriching B-rep attributed adjacency graphs with manufacturing features recognized through a rule-based module. Applied to sheet metal bending, recognized features, such as bend characteristics, flange lengths, and surface roles are integrated as node attributes, concentrating the learning signal on process-relevant geometric patterns. Experiments on both a large-scale synthetic manufacturability benchmark and a real-world industrial dataset with measured bending times, one of the first such validations on genuine production data, demonstrate that combining domain knowledge with graph-based learning improves prediction accuracy across both tasks. The results demonstrate that hybrid modeling offers a feasible and effective path toward deployable tools for manufacturability assessment and effort estimation in industrial CAD environments.

preprint2024arXiv

From Invariant Decomposition to Spinors

Plane-based Geometric Algebra (PGA) has revealed points in a $d$-dimensional pseudo-Euclidean space $\mathbb{R}_{p,q,1}$ to be represented by $d$-blades rather than vectors. This discovery allows points to be factored into $d$ orthogonal hyperplanes, establishing points as pseudoscalars of a local geometric algebra $\mathbb{R}_{pq}$. Astonishingly, the non-uniqueness of this factorization reveals the existence of a local $\text{Spin}(p,q)$ geometric gauge group at each point. Moreover, a point can alternatively be factored into a product of the elements of the Cartan subalgebra of $\mathfrak{spin}(p,q)$, which are traditionally used to label spinor representations. Therefore, points reveal previously hidden geometric foundations for some of quantum field theory's mysteries. This work outlines the impact of PGA on the study of spinor representations in any number of dimensions, and is the first in a research programme exploring the consequences of this insight.

preprint2022arXiv

Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball

The estimation of the Källén-Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an appropriate inversion method. As proof of concept the SU(2) glueball spectrum for the quantum numbers $J^{PC} = 0^{++}$ is investigated for various values of the lattice spacing. The spectral density and the glueball spectrum are estimated using the published data of arXiv:1910.07756. Our estimates for the ground state mass are in good agreement with the traditional approach published therein, which is based on the large time exponential behaviour of the correlation functions. Furthermore, the spectral density also contains hints of excites states in the spectrum.

preprint2022arXiv

Normalization, Square Roots, and the Exponential and Logarithmic Maps in Geometric Algebras of Less than 6D

Geometric algebras of dimension $n < 6$ are becoming increasingly popular for the modeling of 3D and 3+1D geometry. With this increased popularity comes the need for efficient algorithms for common operations such as normalization, square roots, and exponential and logarithmic maps. The current work presents a signature agnostic analysis of these common operations in all geometric algebras of dimension $n < 6$, and gives efficient numerical implementations in the most popular algebras $\mathbb{R}_{4}$, $\mathbb{R}_{3,1}$, $\mathbb{R}_{3,0,1}$ and $\mathbb{R}_{4,1}$, in the hopes of lowering the threshold for adoption of geometric algebra solutions by code maintainers.

preprint2022arXiv

Novel algorithm for the computation of group and energy velocities of Lamb waves

A new solution strategy for quadratic eigenvalue problems, and the derivatives of the eigenvalues, is proposed, by combining the generalized reduction method with dual numbers. To demonstrate the method, we use the quadratic eigenvalue problem encountered in the semi-analytical finite element method (SAFE) as a guiding example. The SAFE method is designed to calculate the spectrum of Lamb wave phase, group and energy velocities in (visco)elastic orthotropic media, over a wide frequency range. It was found that the new approach essentially doubles the computational speed and efficiency, without sacrificing accuracy.

preprint2020arXiv

Spectral representation of lattice gluon and ghost propagators at zero temperature

We consider the analytic continuation of Euclidean propagator data obtained from 4D simulations to Minkowski space. In order to perform this continuation, the common approach is to first extract the Källén-Lehmann spectral density of the field. Once this is known, it can be extended to Minkowski space to yield the Minkowski propagator. However, obtaining the Källén-Lehmann spectral density from propagator data is a well known ill-posed numerical problem. To regularize this problem we implement an appropriate version of Tikhonov regularization supplemented with the Morozov discrepancy principle. We will then apply this to various toy model data to demonstrate the conditions of validity for this method, and finally to zero temperature gluon and ghost lattice QCD data. We carefully explain how to deal with the IR singularity of the massless ghost propagator. We also uncover the numerically different performance when using two ---mathematically equivalent--- versions of the Källén-Lehmann spectral integral.