arXiv subjects

Markus Lange-Hegermann

Publications and source records attributed to Markus Lange-Hegermann.

At least 19 recordsLinked to original sources

arXiv2026

ECLASS-Augmented Semantic Product Search for Electronic Components

Efficient semantic access to industrial product data is a key enabler for factory automation and emerging LLM-based agent workflows, where both human engineers and autonomous agents must identify suitable components from highly structured catalogs. However, the vocabulary mismatch between natural-language queries and attribute-centric product descriptions limits the effectiveness of traditional retrieval approaches, e.g., BM25. In this work, we present a systematic evaluation of LLM-assisted dense retrieval for semantic product search on industrial electronic components, and investigate the integration of hierarchical semantics from the ECLASS standard into embedding-based retrieval. Our results show that dense retrieval combined with re-ranking substantially outperforms classical lexical methods and foundation model web-search baselines. In particular, the proposed approach achieves a Hit_Rate@5 of 94.3 %, compared to 31.4 % for BM25 on expert queries, while also exceeding foundation model baselines in both effectiveness and efficiency. Furthermore, augmenting product representations with ECLASS semantics yields consistent performance gains across configurations, demonstrating that standardized hierarchical metadata provides a crucial semantic bridge between user intent and sparse product descriptions.

cs.IR↗

arXiv2026

Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data

We introduce FLASH-MAX, a shallow, exact-by-construction neural network architecture for predicting homogeneous electromagnetic fields from sparse pointwise observations. Each hidden neuron represents a separate exact solution to Maxwell's equations, so that the network satisfies the governing equations symbolically by construction and can be trained end-to-end from sparse data within seconds. We prove a universal approximation result showing that this exact model class remains universal on arbitrary domains. FLASH-MAX reaches sub-1% relative validation error from about 1K sparse pointwise observations in seconds, all while maintaining a zero PDE residual, and keeps single-digit errors even for only 100 observations sampled from 3D space. These results suggest that moving governing structure from the loss into the hypothesis class can dramatically improve the trade-off between precision and optimization speed in scientific machine learning.

cs.LG↗

arXiv2026

Approximately Equivariant Recurrent Generative Models for Quasi-Periodic Time Series with a Progressive Training Scheme

We present a simple yet effective generative model for time series, based on a Recurrent Variational Autoencoder that we refer to as AEQ-RVAE-ST. Recurrent layers often struggle with unstable optimization and poor convergence when modeling long sequences. To address these limitations, we introduce a training scheme that subsequently increases the sequence length, stabilizing optimization and enabling consistent learning over extended horizons. By composing known components into a recurrent, approximately time-shift-equivariant topology, our model introduces an inductive bias that aligns with the structure of quasi-periodic and nearly stationary time series. Across several benchmark datasets, AEQ-RVAE-ST matches or surpasses state-of-the-art generative models, particularly on quasi-periodic data, while remaining competitive on more irregular signals. Performance is evaluated through ELBO, Fréchet Distance, discriminative metrics, and visualizations of the learned latent embeddings.

cs.LG↗

arXiv2025

Investigation of the Impact of Synthetic Training Data in the Industrial Application of Terminal Strip Object Detection

In industrial manufacturing, deploying deep learning models for visual inspection is mostly hindered by the high and often intractable cost of collecting and annotating large-scale training datasets. While image synthesis from 3D CAD models is a common solution, the individual techniques of domain and rendering randomization to create rich synthetic training datasets have been well studied mainly in simple domains. Hence, their effectiveness on complex industrial tasks with densely arranged and similar objects remains unclear. In this paper, we investigate the sim-to-real generalization performance of standard object detectors on the complex industrial application of terminal strip object detection, carefully combining randomization and domain knowledge. We describe step-by-step the creation of our image synthesis pipeline that achieves high realism with minimal implementation effort and explain how this approach could be transferred to other industrial settings. Moreover, we created a dataset comprising 30.000 synthetic images and 300 manually annotated real images of terminal strips, which is publicly available for reference and future research. To provide a baseline as a lower bound of the expectable performance in these challenging industrial parts detection tasks, we show the sim-to-real generalization performance of standard object detectors on our dataset based on a fully synthetic training. While all considered models behave similarly, the transformer-based DINO model achieves the best score with 98.40 % mean average precision on the real test set, demonstrating that our pipeline enables high quality detections in complex industrial environments from existing CAD data and with a manageable image synthesis effort.

cs.CV↗

arXiv2025

Physics-informed Gaussian Processes as Linear Model Predictive Controller with Constraint Satisfaction

Model Predictive Control evolved as the state of the art paradigm for safety critical control tasks. Control-as-Inference approaches thereof model the constrained optimization problem as a probabilistic inference problem. The constraints have to be implemented into the inference model. A recently introduced physics-informed Gaussian Process method uses Control-as-Inference with a Gaussian likelihood for state constraint modeling, but lacks guarantees of open-loop constraint satisfaction. We mitigate the lack of guarantees via an additional sampling step using Hamiltonian Monte Carlo sampling in order to obtain safe rollouts of the open-loop dynamics which are then used to obtain an approximation of the truncated normal distribution which has full probability mass in the safe area. We provide formal guarantees of constraint satisfaction while maintaining the ODE structure of the Gaussian Process on a discretized grid. Moreover, we show that we are able to perform optimization of a quadratic cost function by closed form Gaussian Process computations only and introduce the Matérn kernel into the inference model.

math.OC↗

arXiv2025

Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Parity

We present a new benchmarking study comparing a boundary-constrained Ehrenpreis--Palamodov Gaussian Process (B-EPGP) surrogate with a classical finite element method combined with Crank--Nicolson time stepping (CN-FEM) for solving the two-dimensional wave equation with homogeneous Dirichlet boundary conditions. The B-EPGP construction leverages exponential-polynomial bases derived from the characteristic variety to enforce the PDE and boundary conditions exactly and employs penalized least squares to estimate the coefficients. To ensure fairness across paradigms, we introduce a degrees-of-freedom (DoF) matching protocol. Under matched DoF, B-EPGP consistently attains lower space-time $L^2$-error and maximum-in-time $L^{2}$-error in space than CN-FEM, improving accuracy by roughly two orders of magnitude.

cs.LG↗

arXiv2025

Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equations

Working with systems of partial differential equations (PDEs) is a fundamental task in computational science. Well-posed systems are addressed by numerical solvers or neural operators, whereas systems described by data are often addressed by PINNs or Gaussian processes. In this work, we propose Boundary Ehrenpreis--Palamodov Gaussian Processes (B-EPGPs), a novel probabilistic framework for constructing GP priors that satisfy both general systems of linear PDEs with constant coefficients and linear boundary conditions and can be conditioned on a finite data set. We explicitly construct GP priors for representative PDE systems with practical boundary conditions. Formal proofs of correctness are provided and empirical results demonstrating significant accuracy and computational resource improvements over state-of-the-art approaches.

stat.ML↗

arXiv2025

Physics-Informed Diffusion Models for Unsupervised Anomaly Detection in Multivariate Time Series

We propose an unsupervised anomaly detection approach based on a physics-informed diffusion model for multivariate time series data. Over the past years, diffusion model has demonstrated its effectiveness in forecasting, imputation, generation, and anomaly detection in the time series domain. In this paper, we present a new approach for learning the physics-dependent temporal distribution of multivariate time series data using a weighted physics-informed loss during diffusion model training. A weighted physics-informed loss is constructed using a static weight schedule. This approach enables a diffusion model to accurately approximate underlying data distribution, which can influence the unsupervised anomaly detection performance. Our experiments on synthetic and real-world datasets show that physics-informed training improves the F1 score in anomaly detection; it generates better data diversity and log-likelihood. Our model outperforms baseline approaches, additionally, it surpasses prior physics-informed work and purely data-driven diffusion models on a synthetic dataset and one real-world dataset while remaining competitive on others.

cs.LG↗

arXiv2025

Physics-informed Gaussian Processes as Linear Model Predictive Controller

We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.

math.OC↗

arXiv2025

Gaussian Process Regression for Inverse Problems in Linear PDEs

This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors defined based on advanced commutative algebra and algebraic analysis. The implementation of these priors is algorithmic and achieved using the Macaulay2 computer algebra software. An example application includes identifying the wave speed from noisy data for classical wave equations, which are widely used in physics. The method achieves high accuracy while enhancing computational efficiency.

stat.ML↗

arXiv2025

Linear ordinary differential equations constrained Gaussian Processes for solving optimal control problems

This paper presents an intrinsic approach for addressing control problems with systems governed by linear ordinary differential equations (ODEs). We use computer algebra to constrain a Gaussian Process on solutions of ODEs. We obtain control functions via conditioning on datapoints. Our approach thereby connects Algebra, Functional Analysis, Machine Learning and Control theory. We discuss the optimality of the control functions generated by the posterior mean of the Gaussian Process. We present numerical examples which underline the practicability of our approach.

math.OC↗

arXiv2025

Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processes

Experimental exploration of high-cost systems with safety constraints, common in engineering applications, is a challenging endeavor. Data-driven models offer a promising solution, but acquiring the requisite data remains expensive and is potentially unsafe. Safe active learning techniques prove essential, enabling the learning of high-quality models with minimal expensive data points and high safety. This paper introduces a safe active learning framework tailored for time-varying systems, addressing drift, seasonal changes, and complexities due to dynamic behavior. The proposed Time-aware Integrated Mean Squared Prediction Error (T-IMSPE) method minimizes posterior variance over current and future states, optimizing information gathering also in the time domain. Empirical results highlight T-IMSPE's advantages in model quality through toy and real-world examples. State of the art Gaussian processes are compatible with T-IMSPE. Our theoretical contributions include a clear delineation which Gaussian process kernels, domains, and weighting measures are suitable for T-IMSPE and even beyond for its non-time aware predecessor IMSPE.

cs.LG↗

arXiv2024

Visual Car Brand Classification by Implementing a Synthetic Image Dataset Creation Pipeline

Recent advancements in machine learning, particularly in deep learning and object detection, have significantly improved performance in various tasks, including image classification and synthesis. However, challenges persist, particularly in acquiring labeled data that accurately represents specific use cases. In this work, we propose an automatic pipeline for generating synthetic image datasets using Stable Diffusion, an image synthesis model capable of producing highly realistic images. We leverage YOLOv8 for automatic bounding box detection and quality assessment of synthesized images. Our contributions include demonstrating the feasibility of training image classifiers solely on synthetic data, automating the image generation pipeline, and describing the computational requirements for our approach. We evaluate the usability of different modes of Stable Diffusion and achieve a classification accuracy of 75%.

cs.CV↗

arXiv2024

PGNAA Spectral Classification of Aluminium and Copper Alloys with Machine Learning

In this paper, we explore the optimization of metal recycling with a focus on real-time differentiation between alloys of copper and aluminium. Spectral data, obtained through Prompt Gamma Neutron Activation Analysis (PGNAA), is utilized for classification. The study compares data from two detectors, cerium bromide (CeBr$_{3}$) and high purity germanium (HPGe), considering their energy resolution and sensitivity. We test various data generation, preprocessing, and classification methods, with Maximum Likelihood Classifier (MLC) and Conditional Variational Autoencoder (CVAE) yielding the best results. The study also highlights the impact of different detector types on classification accuracy, with CeBr$_{3}$ excelling in short measurement times and HPGe performing better in longer durations. The findings suggest the importance of selecting the appropriate detector and methodology based on specific application requirements.

cs.LG↗

arXiv2024

Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning

Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this purpose. In many technical applications the design space is explored via continuous trajectories, along which the safety needs to be assessed. This is particularly challenging for strict safety requirements in GP methods, as it employs computationally expensive Monte-Carlo sampling of high quantiles. We address these challenges by providing provable safety bounds based on the adaptively sampled median of the supremum of the posterior GP. Our method significantly reduces the number of samples required for estimating high safety probabilities, resulting in faster evaluation without sacrificing accuracy and exploration speed. The effectiveness of our safe active learning approach is demonstrated through extensive simulations and validated using a real-world engine example.

cs.LG↗

arXiv2024

On the Laplace Approximation as Model Selection Criterion for Gaussian Processes

Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides the best trade-off between all those criteria. While previous work considers metrics like the likelihood, AIC or dynamic nested sampling, they either lack performance or have significant runtime issues, which severely limits applicability. We address these challenges by introducing multiple metrics based on the Laplace approximation, where we overcome a severe inconsistency occuring during naive application of the Laplace approximation. Experiments show that our metrics are comparable in quality to the gold standard dynamic nested sampling without compromising for computational speed. Our model selection criteria allow significantly faster and high quality model selection of Gaussian process models.

cs.LG↗

arXiv2023

Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients

Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works as a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDEs, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

stat.ML↗

arXiv2023

Interpretable Anomaly Detection in Cellular Networks by Learning Concepts in Variational Autoencoders

This paper addresses the challenges of detecting anomalies in cellular networks in an interpretable way and proposes a new approach using variational autoencoders (VAEs) that learn interpretable representations of the latent space for each Key Performance Indicator (KPI) in the dataset. This enables the detection of anomalies based on reconstruction loss and Z-scores. We ensure the interpretability of the anomalies via additional information centroids (c) using the K-means algorithm to enhance representation learning. We evaluate the performance of the model by analyzing patterns in the latent dimension for specific KPIs and thereby demonstrate the interpretability and anomalies. The proposed framework offers a faster and autonomous solution for detecting anomalies in cellular networks and showcases the potential of deep learning-based algorithms in handling big data.

cs.LG↗