arXiv subjects

Alexander Haberl

Publications and source records attributed to Alexander Haberl.

16 recordsLinked to original sources

arXiv2026

Fast Time-Domain MLE for Period Estimation of Pulse Trains

Parameter estimation of periodic pulse trains is a critical task in numerous automated sensing and diagnostic applications. While estimation in the time domain provides superior accuracy in low signal-to-noise ratio environments, its high computational complexity frequently precludes its use in real-time systems. This paper investigates algorithmic optimizations to reduce runtime by leveraging recent advancements in computing architectures. Exploiting the inherent sparsity of the signal via sparse matrix multiplication kernels yields a substantial decrease in inference time. Furthermore, by separating the dense matrix projections into sequential cross-correlation and sparse summation steps, we fundamentally reduce both runtime and memory complexity. These optimizations drastically shrink the memory footprint, making time-domain estimation feasible for large datasets in real-time settings.

eess.SP↗

arXiv2025

POMDP-Based Routing for DTNs with Partial Knowledge and Dependent Failures

Routing in Delay-Tolerant Networks (DTNs) is inherently challenging due to sparse connectivity, long delays, and frequent disruptions. While Markov Decision Processes (MDPs) have been used to model uncertainty, they assume full state observability - an assumption that breaks down in partitioned DTNs, where each node operates with inherently partial knowledge of the network state. In this work, we investigate the role of Partially Observable Markov Decision Processes (POMDPs) for DTN routing under uncertainty. We introduce and evaluate a novel model: Dependent Node Failures (DNF), which captures correlated node failures via repairable node states modeled as Continuous-Time Markov Chains (CTMCs). We implement the model using JuliaPOMDP and integrate it with DTN simulations via DtnSim. Our evaluation demonstrates that POMDP-based routing yields improved delivery ratios and delay performance under uncertain conditions while maintaining scalability. These results highlight the potential of POMDPs as a principled foundation for decision-making in future DTN deployments.

cs.NI↗

arXiv2025

Estimators and Performance Bounds for Short Periodic Pulses

In many industrial applications, signals with short periodic pulses, caused by repeated steps in the manufacturing process, are present, and their fundamental frequency or period may be of interest. Fundamental frequency estimation is in many cases performed by describing the periodic signal as a multiharmonic signal and employing the corresponding maximum likelihood estimator. However, since signals with short periodic pulses contain a large number of noise-only samples, the multiharmonic signal model is not optimal to describe them. In this work, two models of short periodic pulses with known and unknown pulse shape are considered. For both models, the corresponding maximum likelihood estimators, Fisher information matrices, and approximate Cram\'er-Rao lower bounds are presented. Numerical results demonstrate that the proposed estimators outperform the maximum likelihood estimator based on the multiharmonic signal model for low signal-to-noise ratios.

eess.SP↗

arXiv2025

InCoRe -- An Interactive Co-Regulation Model: Training Teacher Communication Skills in Demanding Classroom Situations

Socioemotional and regulation processes in learning are important. We add to the understanding of previous work on co-regulation processes in the learning sciences, extending the caregiver-child paradigm and focusing on the teacher-student relation by presenting an interactive co-regulation model and the methodology for developing empirically grounded systems for training teachers. We focus on the combination of classroom management and affect models and detail the use of a psychological model to operationalise and automate the interaction with the virtual student. We delve into an annotation scheme developed to capture teacher subjective psychological experiences during training and how these affect their co-regulation behavior with students and contributes to understanding the role of teacher emotional experiences and their consequences of co-regulation processes for classroom management. This research is also a contribution to developing hybrid AI systems.

cs.HC↗

arXiv2024

ReFlow6D: Refraction-Guided Transparent Object 6D Pose Estimation via Intermediate Representation Learning

Transparent objects are ubiquitous in daily life, making their perception and robotics manipulation important. However, they present a major challenge due to their distinct refractive and reflective properties when it comes to accurately estimating the 6D pose. To solve this, we present ReFlow6D, a novel method for transparent object 6D pose estimation that harnesses the refractive-intermediate representation. Unlike conventional approaches, our method leverages a feature space impervious to changes in RGB image space and independent of depth information. Drawing inspiration from image matting, we model the deformation of the light path through transparent objects, yielding a unique object-specific intermediate representation guided by light refraction that is independent of the environment in which objects are observed. By integrating these intermediate features into the pose estimation network, we show that ReFlow6D achieves precise 6D pose estimation of transparent objects, using only RGB images as input. Our method further introduces a novel transparent object compositing loss, fostering the generation of superior refractive-intermediate features. Empirical evaluations show that our approach significantly outperforms state-of-the-art methods on TOD and Trans32K-6D datasets. Robot grasping experiments further demonstrate that ReFlow6D's pose estimation accuracy effectively translates to real-world robotics task. The source code is available at: https://github.com/StoicGilgamesh/ReFlow6D and https://github.com/StoicGilgamesh/matting_rendering.

cs.CV↗

arXiv2024

Robustness of Explainable Artificial Intelligence in Industrial Process Modelling

eXplainable Artificial Intelligence (XAI) aims at providing understandable explanations of black box models. In this paper, we evaluate current XAI methods by scoring them based on ground truth simulations and sensitivity analysis. To this end, we used an Electric Arc Furnace (EAF) model to better understand the limits and robustness characteristics of XAI methods such as SHapley Additive exPlanations (SHAP), Local Interpretable Model-agnostic Explanations (LIME), as well as Averaged Local Effects (ALE) or Smooth Gradients (SG) in a highly topical setting. These XAI methods were applied to various types of black-box models and then scored based on their correctness compared to the ground-truth sensitivity of the data-generating processes using a novel scoring evaluation methodology over a range of simulated additive noise. The resulting evaluation shows that the capability of the Machine Learning (ML) models to capture the process accurately is, indeed, coupled with the correctness of the explainability of the underlying data-generating process. We furthermore show the differences between XAI methods in their ability to correctly predict the true sensitivity of the modeled industrial process.

cs.LG↗

arXiv2020

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

We consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation interconnecting a finite element discretization, the Banach-Picard linearization, and a contractive linear algebraic solver. We in particular identify stopping criteria for the algebraic solver that on the one hand do not request an overly tight tolerance but on the other hand are sufficient for the inexact (perturbed) Banach-Picard linearization to remain contractive. Similarly, we identify suitable stopping criteria for the Banach-Picard iteration that leave an amount of linearization error that is not harmful for the residual a-posteriori error estimate to steer reliably the adaptive mesh-refinement. For the resulting algorithm, we prove a contraction of the (doubly) inexact iterates after some amount of steps of mesh-refinement / linerization / algebraic solver, leading to its linear convergence. Moreover, for usual mesh-refinement rules, we also prove that the overall error decays at the optimal rate with respect to the number of elements (degrees of freedom) added with respect to the initial mesh. Finally, we prove that our fully adaptive algorithm drives the overall error down with the same optimal rate also with respect to the overall algorithmic cost expressed as the cumulated sum of the number of mesh elements over all mesh-refinement, linearization, and algebraic solver steps. Numerical experiments support these theoretical findings and illustrate the optimal overall algorithmic cost of the fully adaptive algorithm on several test cases.

math.NA↗

arXiv2020

Rate optimality of adaptive finite element methods with respect to the overall computational costs

We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the adaptive mesh-refinement as well as the inexact solution of the arising discrete systems. We prove that the proposed strategy leads to linear convergence with optimal algebraic rates. Unlike prior works, however, we focus on convergence rates with respect to the overall computational costs. In explicit terms, the proposed adaptive strategy thus guarantees quasi-optimal computational time. In particular, our analysis covers linear problems, where the linear systems are solved by an optimally preconditioned CG method as well as nonlinear problems with strongly monotone nonlinearity which are linearized by the so-called Zarantonello iteration.

math.NA↗

arXiv2019

Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra

The accurate computation of the electrostatic capacity of three dimensional objects is a fascinating benchmark problem with a long and rich history. In particular, the capacity of the unit cube has widely been studied, and recent advances allow to compute its capacity to more than ten digits of accuracy. However, the accurate computation of the capacity for general three dimensional polyhedra is still an open problem. In this paper, we propose a new algorithm based on a combination of ZZ-type a posteriori error estimation and effective operator preconditioned boundary integral formulations to easily compute the capacity of complex three dimensional polyhedra to 5 digits and more. While this paper focuses on the capacity as a benchmark problem, it also discusses implementational issues of adaptive boundary element solvers, and we provide codes based on the boundary element package Bempp to make the underlying techniques accessible to a wide range of practical problems.

math.NA↗

arXiv2019

Trace operators of the bi-Laplacian and applications

We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are also relevant to describe conformity of mixed approximations. Our aim is to have well-posed (ultraweak) formulations that assume low regularity, under the condition of an $L_2$ right-hand side function. We pursue two ways of defining traces and corresponding integration-by-parts formulas. In one case one obtains a non-closed space. This can be fixed by switching to the Kirchhoff-Love traces from [F\"uhrer, Heuer, Niemi, An ultraweak formulation of the Kirchhoff-Love plate bending model and DPG approximation, Math. Comp., 88 (2019)]. Using different combinations of trace operators we obtain two well-posed formulations. For both of them we report on numerical experiments with the DPG method and optimal test functions. In this paper we consider two and three space dimensions. However, with the exception of a given counterexample in an appendix (related to the non-closedness of a trace space), our analysis applies to any space dimension larger than or equal to two.

math.NA↗

arXiv2018

Adaptive BEM with optimal convergence rates for the Helmholtz equation

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation.

math.NA↗

arXiv2018

Adaptive BEM with inexact PCG solver yields almost optimal computational costs

We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as well as the local mesh-refinement. Besides convergence with optimal algebraic rates, we also prove almost optimal computational complexity. In particular, we provide an additive Schwarz preconditioner which can be computed in linear complexity and which is optimal in the sense that the condition numbers of the preconditioned systems are uniformly bounded. As model problem serves the 2D or 3D Laplace operator and the associated weakly-singular integral equation with energy space $\widetilde{H}^{-1/2}(\Gamma)$. The main results also hold for the hyper-singular integral equation with energy space $H^{1/2}(\Gamma)$.

math.NA↗

arXiv2016

Rate optimal adaptive FEM with inexact solver for nonlinear operators

We prove convergence with optimal algebraic rates for an adaptive finite element method for nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also includes the iterative and inexact solution of the arising nonlinear systems by means of the Picard iteration. Using nested iteration, we prove, in particular, that the number of of Picard iterations is uniformly bounded in generic cases, and the overall computational cost is (almost) optimal. Numerical experiments confirm the theoretical results.

math.NA↗

arXiv2016

Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems

We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates. As an important consequence of our analysis, one does not have to deal with the a-priori assumption that the underlying meshes are sufficiently fine. Hence, the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes. In particular, our analysis covers adaptive mesh-refinement for the finite element discretization of the Helmholtz equation from where our interest originated.

math.NA↗

arXiv2015

Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations

In a recent work, we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity of the knots. In the present work, we give a mathematical proof that this algorithm leads to convergence even with optimal algebraic rates. Technical contributions include a novel mesh-size function which also monitors the knot multiplicity as well as inverse estimates for NURBS in fractional-order Sobolev norms.

math.NA↗

arXiv2015

Adaptive 2D IGA boundary element methods

We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error estimator for Galerkin IGA boundary element methods, the present work focuses more on collocation and weighted- residual error estimators, which provide reliable upper bounds for the energy error. Our analysis allows piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. We formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments show that the proposed adaptive strategy leads to optimal convergence, and related IGA boundary element methods are superior to standard boundary element methods with piecewise polynomials.

math.NA↗