arXiv subjects

Stephan Chalup

Publications and source records attributed to Stephan Chalup.

9 recordsLinked to original sources

arXiv2025

Challenges in 3D Data Synthesis for Training Neural Networks on Topological Features

Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural network-based estimators capable of reducing computational overhead and inference time. A key barrier to advancing these methods is the lack of labeled 3D data with class distributions and diversity tailored specifically for supervised learning in TDA tasks. To address this, we introduce a novel approach for systematically generating labeled 3D datasets using the Repulsive Surface algorithm, allowing control over topological invariants, such as hole count. The resulting dataset offers varied geometry with topological labeling, making it suitable for training and benchmarking neural network estimators. This paper uses a synthetic 3D dataset to train a genus estimator network, created using a 3D convolutional transformer architecture. An observed decrease in accuracy as deformations increase highlights the role of not just topological complexity, but also geometric complexity, when training generalized estimators. This dataset fills a gap in labeled 3D datasets and generation for training and evaluating models and techniques for TDA.

cs.CV↗

arXiv2025

Noise-Robust Topology Estimation of 2D Image Data via Neural Networks and Persistent Homology

Persistent Homology (PH) and Artificial Neural Networks (ANNs) offer contrasting approaches to inferring topological structure from data. In this study, we examine the noise robustness of a supervised neural network trained to predict Betti numbers in 2D binary images. We compare an ANN approach against a PH pipeline based on cubical complexes and the Signed Euclidean Distance Transform (SEDT), which is a widely adopted strategy for noise-robust topological analysis. Using one synthetic and two real-world datasets, we show that ANNs can outperform this PH approach under noise, likely due to their capacity to learn contextual and geometric priors from training data. Though still emerging, the use of ANNs for topology estimation offers a compelling alternative to PH under structural noise.

cs.CV↗

arXiv2025

Time Series Analysis of Spiking Neural Systems via Transfer Entropy and Directed Persistent Homology

We present a topological framework for analysing neural time series that integrates Transfer Entropy (TE) with directed Persistent Homology (PH) to characterize information flow in spiking neural systems. TE quantifies directional influence between neurons, producing weighted, directed graphs that reflect dynamic interactions. These graphs are then analyzed using PH, enabling assessment of topological complexity across multiple structural scales and dimensions. We apply this TE+PH pipeline to synthetic spiking networks trained on logic gate tasks, image-classification networks exposed to structured and perturbed inputs, and mouse cortical recordings annotated with behavioral events. Across all settings, the resulting topological signatures reveal distinctions in task complexity, stimulus structure, and behavioral regime. Higher-dimensional features become more prominent in complex or noisy conditions, reflecting interaction patterns that extend beyond pairwise connectivity. Our findings offer a principled approach to mapping directed information flow onto global organizational patterns in both artificial and biological neural systems. The framework is generalizable and interpretable, making it well suited for neural systems with time-resolved and binary spiking data.

q-bio.NC↗

arXiv2025

Simultaneous layout and device parameter optimisation of a wave energy park in an irregular sea

The design of optimal wave energy parks, namely, arrays of devices known as wave energy converters (WECs) that extract energy from water waves, is an important consideration for the renewable transition. In this paper, the problem of simultaneously optimising the layout and device parameters of a wave energy park is considered within the framework of linear water wave theory. Each WEC is modelled as a heaving truncated cylinder coupled to a spring-damper power take-off. The single-WEC scattering problem is solved using an integral equation/Galerkin method, and interactions between the WECs are solved via a self-consistent multiple scattering theory. The layout of the array and power take-off parameters of its constituent devices are simultaneously optimised using a genetic algorithm, with the goal of maximising energy absorption under a unidirectional, irregular sea described by a Pierson--Moskowitz spectrum. When constrained to a rectangular bounding box that is elongated in the direction of wave propagation, the optimal arrays consist of graded pseudo-line arrays when the number of WECs is sufficiently large. Moreover, low-frequency waves propagate further into the array than high-frequency waves, which is indicative of rainbow absorption, namely, the effect wherein waves spatially separate in a graded array based on their frequency, and are preferentially absorbed at these locations. Arrays optimised for a square bounding box did not show strong evidence of grading or rainbow reflection, which indicates that more complicated interaction effects are present.

physics.flu-dyn↗

arXiv2024

A Benchmark of Generative Methods for Zero-Shot Environmental Sound Classification

Zero-shot learning enables models to generalise to unseen classes using semantic information, bridging the gap between training classes and previously unseen test classes. While widely studied in computer vision, its application to environmental audio remains underexplored, and generative approaches have received little attention. This work presents the first benchmark of generative methods for zero-shot environmental sound classification. Four approaches spanning variational, adversarial, diffusion-based, and denoising paradigms are evaluated. The benchmark includes CADA-VAE and LisGAN, adapted from computer vision, together with two embedding-generation methods introduced in this work: one based on a denoising diffusion probabilistic model (DDPM) and the other on a conditional generative denoising network (CGDN). Experiments on five environmental audio datasets (ESC-50, ARCA23K-FSD, FSC22, UrbanSound8K, and TAU Urban Acoustic Scenes 2019) and one music dataset (GTZAN) show that generative methods are competitive with established compatibility-based approaches. Among the evaluated generative methods, CGDN achieves the highest average accuracy and is the only one to significantly outperform both the DDPM- and GAN-based methods, while remaining statistically indistinguishable from the strong ALE baseline. These findings suggest that optimisation stability is an important factor in generative zero-shot learning for environmental audio.

cs.SD↗

arXiv2024

Generating Topologically and Geometrically Diverse Manifold Data in Dimensions Four and Below

Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological features in these data. These models also appear to tolerate the use of image preprocessing techniques where existing topological data analysis techniques such as persistent homology do not. This paper investigates how methods from algebraic topology, combined with image processing techniques such as morphology, can be used to generate topologically sophisticated and diverse-looking 2-, 3-, and 4D image-type data with topological labels in simulation. These approaches are illustrated in 2D and 3D with the aim of providing a roadmap towards achieving this in 4D.

cs.CV↗

arXiv2023

Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the genus of these manifolds. This data used random homeomorphic deformations to provoke the learning of visual topological features. We demonstrate that deep learning models could extract these features and discuss some advantages over existing topological data analysis tools that are based on persistent homology. Semantic segmentation was used to provide additional geometric information in conjunction with topological labels. Common point cloud multi-layer perceptron and transformer networks were both used to compare the viability of these methods. The experimental results of this pilot study support the hypothesis that, with the aid of sophisticated synthetic data generation, neural networks can perform segmentation-based topological data analysis. While our study focused on simulated data, the accuracy achieved suggests a potential for future applications using real data.

cs.CV↗

arXiv2023

The Director: A Composable Behaviour System with Soft Transitions

Software frameworks for behaviour are critical in robotics as they enable the correct and efficient execution of functions. While modern behaviour systems have improved their composability, they do not focus on smooth transitions and often lack functionality. In this work, we present the Director, a novel behaviour framework that addresses these problems. It has functionality for soft transitions, multiple implementations of the same action chosen based on conditionals, and strict resource control. The system was successfully used in the 2022/2023 Virtual Season and RoboCup 2023 Bordeaux, in the Humanoid Kid Size League. It is implemented at https://github.com/NUbots/DirectorSoccer, which also contains over thirty automated tests and technical documentation on its implementation in NUClear.

cs.RO↗

arXiv2023

Topology Estimation of Simulated 4D Image Data by Combining Downscaling and Convolutional Neural Networks

The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks (CNNs), impractical due to computational constraints. This study aims to estimate the topology type of 4D image-type data cubes that exhibit topological intricateness and size above our current processing capacity. The experiments using synthesised 4D data and a real-world 3D data set demonstrate that it is possible to circumvent computational complexity issues by applying downscaling methods to the data before training a CNN. This is achievable even when persistent homology software indicates that downscaling can significantly alter the homology of the training data. When provided with downscaled test data, the CNN can still estimate the Betti numbers of the original sample cubes with over 80\% accuracy, which outperforms the persistent homology approach, whose accuracy deteriorates under the same conditions. The accuracy of the CNNs can be further increased by moving from a mathematically-guided approach to a more vision-based approach where cavity types replace the Betti numbers as training targets.

cs.CV↗