arXiv subjects

Heike Leitte

Publications and source records attributed to Heike Leitte.

At least 19 recordsLinked to original sources

arXiv2025

Formally Exploring Time-Series Anomaly Detection Evaluation Metrics

Undetected anomalies in time series can trigger catastrophic failures in safety-critical systems, such as chemical plant explosions or power grid outages. Although many detection methods have been proposed, their performance remains unclear because current metrics capture only narrow aspects of the task and often yield misleading results. We address this issue by introducing verifiable properties that formalize essential requirements for evaluating time-series anomaly detection. These properties enable a theoretical framework that supports principled evaluations and reliable comparisons. Analyzing 37 widely used metrics, we show that most satisfy only a few properties, and none satisfy all, explaining persistent inconsistencies in prior results. To close this gap, we propose LARM, a flexible metric that provably satisfies all properties, and extend it to ALARM, an advanced variant meeting stricter requirements.

cs.LG↗

arXiv2025

Batch Distillation Data for Developing Machine Learning Anomaly Detection Methods

Machine learning (ML) holds great potential to advance anomaly detection (AD) in chemical processes. However, the development of ML-based methods is hindered by the lack of openly available experimental data. To address this gap, we have set up a laboratory-scale batch distillation plant and operated it to generate an extensive experimental database, covering fault-free experiments and experiments in which anomalies were intentionally induced, for training advanced ML-based AD methods. In total, 119 experiments were conducted across a wide range of operating conditions and mixtures. Most experiments containing anomalies were paired with a corresponding fault-free one. The database that we provide here includes time-series data from numerous sensors and actuators, along with estimates of measurement uncertainty. In addition, unconventional data sources -- such as concentration profiles obtained via online benchtop NMR spectroscopy and video and audio recordings -- are provided. Extensive metadata and expert annotations of all experiments are included. The anomaly annotations are based on an ontology developed in this work. The data are organized in a structured database and made freely available via doi.org/10.5281/zenodo.17395543. This new database paves the way for the development of advanced ML-based AD methods. As it includes information on the causes of anomalies, it further enables the development of interpretable and explainable ML approaches, as well as methods for anomaly mitigation.

cs.LG↗

arXiv2025

Superstudent intelligence in thermodynamics

In this short note, we report and analyze a striking event: OpenAI's large language model o3 has outwitted all students in a university exam on thermodynamics. The thermodynamics exam is a difficult hurdle for most students, where they must show that they have mastered the fundamentals of this important topic. Consequently, the failure rates are very high, A-grades are rare - and they are considered proof of the students' exceptional intellectual abilities. This is because pattern learning does not help in the exam. The problems can only be solved by knowledgeably and creatively combining principles of thermodynamics. We have given our latest thermodynamics exam not only to the students but also to OpenAI's most powerful reasoning model, o3, and have assessed the answers of o3 exactly the same way as those of the students. In zero-shot mode, the model o3 solved all problems correctly, better than all students who took the exam; its overall score was in the range of the best scores we have seen in more than 10,000 similar exams since 1985. This is a turning point: machines now excel in complex tasks, usually taken as proof of human intellectual capabilities. We discuss the consequences this has for the work of engineers and the education of future engineers.

cs.CE↗

arXiv2025

Using Large Language Models for Solving Thermodynamic Problems

Large Language Models (LLMs) have made significant progress in reasoning, demonstrating their capability to generate human-like responses. This study analyzes the problem-solving capabilities of LLMs in the domain of thermodynamics. A benchmark of 22 thermodynamic problems to evaluate LLMs is presented that contains both simple and advanced problems. Five different LLMs are assessed: GPT-3.5, GPT-4, and GPT-4o from OpenAI, Llama 3.1 from Meta, and le Chat from MistralAI. The answers of these LLMs were evaluated by trained human experts, following a methodology akin to the grading of academic exam responses. The scores and the consistency of the answers are discussed, together with the analytical skills of the LLMs. Both strengths and weaknesses of the LLMs become evident. They generally yield good results for the simple problems, but also limitations become clear: The LLMs do not provide consistent results, they often fail to fully comprehend the context and make wrong assumptions. Given the complexity and domain-specific nature of the problems, the statistical language modeling approach of the LLMs struggles with the accurate interpretation and the required reasoning. The present results highlight the need for more systematic integration of thermodynamic knowledge with LLMs, for example, by using knowledge-based methods.

cs.CE↗

arXiv2025

Accelerating Computation of Stable Merge Tree Edit Distances using Parameterized Heuristics

In this paper, we present a novel heuristic algorithm for the stable but NP-complete deformation-based edit distance on merge trees. Our key contribution is the introduction of a user-controlled look-ahead parameter that allows to trade off accuracy and computational cost. We achieve a fixed parameter tractable running time that is polynomial in the size of the input but exponential in the look-ahead value. This extension unlocks the potential of the deformation-based edit distance in handling saddle swaps, while maintaining feasible computation times. Experimental results demonstrate the computational efficiency and effectiveness of this approach in handling specific perturbations.

cs.CG↗

arXiv2024

Hierarchical Matrix Completion for the Prediction of Properties of Binary Mixtures

Predicting the thermodynamic properties of mixtures is crucial for process design and optimization in chemical engineering. Machine learning (ML) methods are gaining increasing attention in this field, but experimental data for training are often scarce, which hampers their application. In this work, we introduce a novel generic approach for improving data-driven models: inspired by the ancient rule "similia similibus solvuntur", we lump components that behave similarly into chemical classes and model them jointly in the first step of a hierarchical approach. While the information on class affiliations can stem in principle from any source, we demonstrate how classes can reproducibly be defined based on mixture data alone by agglomerative clustering. The information from this clustering step is then used as an informed prior for fitting the individual data. We demonstrate the benefits of this approach by applying it in connection with a matrix completion method (MCM) for predicting isothermal activity coefficients at infinite dilution in binary mixtures. Using clustering leads to significantly improved predictions compared to an MCM without clustering. Furthermore, the chemical classes learned from the clustering give exciting insights into what matters on the molecular level for modeling given mixture properties.

cs.LG↗

arXiv2024

KnowTD-An Actionable Knowledge Representation System for Thermodynamics

We demonstrate that thermodynamic knowledge acquired by humans can be transferred to computers so that the machine can use it to solve thermodynamic problems and produce explainable solutions with a guarantee of correctness. The actionable knowledge representation system that we have created for this purpose is called KnowTD. It is based on an ontology of thermodynamics that represents knowledge of thermodynamic theory, material properties, and thermodynamic problems. The ontology is coupled with a reasoner that sets up the problem to be solved based on user input, extracts the correct, pertinent equations from the ontology, solves the resulting mathematical problem, and returns the solution to the user, together with an explanation of how it was obtained. KnowTD is presently limited to simple thermodynamic problems, similar to those discussed in an introductory course in Engineering Thermodynamics. This covers the basic theory and working principles of thermodynamics. KnowTD is designed in a modular way and is easily extendable.

cs.CE↗

arXiv2024

Machine Learning Based Optimization Workflow for Tuning Numerical Settings of Differential Equation Solvers for Boundary Value Problems

Several numerical differential equation solvers have been employed effectively over the years as an alternative to analytical solvers to quickly and conveniently solve differential equations. One category of these is boundary value solvers, which are used to solve real-world problems formulated as differential equations with boundary conditions. These solvers require certain numerical settings to solve the differential equations that affect their solvability and performance. A systematic fine-tuning of these settings is required to obtain the desired solution and performance. Currently, these settings are either selected by trial and error or require domain expertise. In this paper, we propose a machine learning-based optimization workflow for fine-tuning the numerical settings to reduce the time and domain expertise required in the process. In the evaluation section, we discuss the scalability, stability, and reliability of the proposed workflow. We demonstrate our workflow on a numerical boundary value problem solver.

math.NA↗

arXiv2024

Machine learning-based optimization workflow of the homogeneity of spunbond nonwovens with human validation

In the last ten years, the average annual growth rate of nonwoven production was 4%. In 2020 and 2021, nonwoven production has increased even further due to the huge demand for nonwoven products needed for protective clothing such as FFP2 masks to combat the COVID19 pandemic. Optimizing the production process is still a challenge due to its high nonlinearity. In this paper, we present a machine learning-based optimization workflow aimed at improving the homogeneity of spunbond nonwovens. The optimization workflow is based on a mathematical model that simulates the microstructures of nonwovens. Based on trainingy data coming from this simulator, different machine learning algorithms are trained in order to find a surrogate model for the time-consuming simulator. Human validation is employed to verify the outputs of machine learning algorithms by assessing the aesthetics of the nonwovens. We include scientific and expert knowledge into the training data to reduce the computational costs involved in the optimization process. We demonstrate the necessity and effectiveness of our workflow in optimizing the homogeneity of nonwovens.

cs.LG↗

arXiv2023

Deep Anomaly Detection on Tennessee Eastman Process Data

This paper provides the first comprehensive evaluation and analysis of modern (deep-learning) unsupervised anomaly detection methods for chemical process data. We focus on the Tennessee Eastman process dataset, which has been a standard litmus test to benchmark anomaly detection methods for nearly three decades. Our extensive study will facilitate choosing appropriate anomaly detection methods in industrial applications.

cs.LG↗

arXiv2022

Branch Decomposition-Independent Edit Distances for Merge Trees

Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the construction of edit mappings for merge trees. Classic edit mappings match nodes or edges of two trees onto each other, and therefore have to either rely on branch decompositions of both trees or have to use auxiliary node properties to determine a matching. In contrast, branch mappings employ branch properties instead of node similarity information, and are independent of predetermined branch decompositions. Especially for topological features, which are typically based on branch properties, this allows a more intuitive distance measure which is also less susceptible to instabilities from small-scale perturbations. We describe a quartic runtime algorithm for computing optimal branch mappings, which is faster than the only other branch decomposition-independent method in the literature by more than a linear factor. Furthermore, we compare the results of our method on synthetic and real-world examples to demonstrate its practicality and utility.

cs.CG↗

arXiv2021

Attribute-based Explanations of Non-Linear Embeddings of High-Dimensional Data

Embeddings of high-dimensional data are widely used to explore data, to verify analysis results, and to communicate information. Their explanation, in particular with respect to the input attributes, is often difficult. With linear projects like PCA the axes can still be annotated meaningfully. With non-linear projections this is no longer possible and alternative strategies such as attribute-based color coding are required. In this paper, we review existing augmentation techniques and discuss their limitations. We present the Non-Linear Embeddings Surveyor (NoLiES) that combines a novel augmentation strategy for projected data (rangesets) with interactive analysis in a small multiples setting. Rangesets use a set-based visualization approach for binned attribute values that enable the user to quickly observe structure and detect outliers. We detail the link between algebraic topology and rangesets and demonstrate the utility of NoLiES in case studies with various challenges (complex attribute value distribution, many attributes, many data points) and a real-world application to understand latent features of matrix completion in thermodynamics.

cs.LG↗

arXiv2021

Knowledge Rocks:Adding Knowledge Assistance to Visualization Systems

We present Knowledge Rocks, an implementation strategy and guideline for augmenting visualization systems to knowledge-assisted visualization systems, as defined by the KAVA model. Visualization systems become more and more sophisticated. Hence, it is increasingly important to support users with an integrated knowledge base in making constructive choices and drawing the right conclusions. We support the effective reactivation of visualization software resources by augmenting them with knowledge-assistance. To provide a general and yet supportive implementation strategy, we propose an implementation process that bases on an application-agnostic architecture. This architecture is derived from existing knowledge-assisted visualization systems and the KAVA model. Its centerpiece is an ontology that is able to automatically analyze and classify input data, linked to a database to store classified instances. We discuss design decisions and advantages of the KR framework and illustrate its broad area of application in diverse integration possibilities of this architecture into an existing visualization system. In addition, we provide a detailed case study by augmenting an it-security system with knowledge-assistance facilities.

cs.HC↗

arXiv2020

Visual Probing and Correction of Object Recognition Models with Interactive user feedback

With the advent of state-of-the-art machine learning and deep learning technologies, several industries are moving towards the field. Applications of such technologies are highly diverse ranging from natural language processing to computer vision. Object recognition is one such area in the computer vision domain. Although proven to perform with high accuracy, there are still areas where such models can be improved. This is in-fact highly important in real-world use cases like autonomous driving or cancer detection, that are highly sensitive and expect such technologies to have almost no uncertainties. In this paper, we attempt to visualise the uncertainties in object recognition models and propose a correction process via user feedback. We further demonstrate our approach on the data provided by the VAST 2020 Mini-Challenge 2.

cs.CV↗

arXiv2019

Security in Process: Visually Supported Triage Analysis in Industrial Process Data

Operation technology networks, i.e. hard- and software used for monitoring and controlling physical/industrial processes, have been considered immune to cyber attacks for a long time. A recent increase of attacks in these networks proves this assumption wrong. Several technical constraints lead to approaches to detect attacks on industrial processes using available sensor data. This setting differs fundamentally from anomaly detection in IT-network traffic and requires new visualization approaches adapted to the common periodical behavior in OT-network data. We present a tailored visualization system that utilizes inherent features of measurements from industrial processes to full capacity to provide insight into the data and support triage analysis by laymen and experts. The novel combination of spiral plots with results from anomaly detection was implemented in an interactive system. The capabilities of our system are demonstrated using sensor and actuator data from a real-world water treatment process with introduced attacks. Exemplary analysis strategies are presented. Finally, we evaluate effectiveness and usability of our system and perform an expert evaluation.

cs.CR↗

arXiv2019

Hierarchies and Ranks for Persistence Pairs

We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persistence pairs. Our work is motivated by a lack of spatial relationships between features in persistence diagrams, leading to a limited expressive power. We build upon a recently-introduced hierarchy of pairs in persistence diagrams that augments the pairing stored in persistence diagrams with information about which components merge. Our proposed hierarchy captures differences in branching structure. Moreover, we show how to use our hierarchy to measure the spatial stability of a pairing and we define a rank function for persistence pairs and demonstrate different applications.

math.AT↗

arXiv2019

Persistent Intersection Homology for the Analysis of Discrete Data

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional manifold. In such cases, persistent homology can be successfully employed to extract features, remove noise, and compare data sets. The underlying problems in some application domains, however, turn out to represent multiple manifolds with different dimensions. Algebraic topology typically analyzes such problems using intersection homology, an extension of homology that is capable of handling configurations with singularities. In this paper, we describe how the persistent variant of intersection homology can be used to assist data analysis in visualization. We point out potential pitfalls in approximating data sets with singularities and give strategies for resolving them.

math.AT↗

arXiv2019

Topological Machine Learning with Persistence Indicator Functions

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional scaling, while providing a firm theoretical ground. Many modern machine learning algorithms, however, are based on kernels. This paper presents persistence indicator functions (PIFs), which summarize persistence diagrams, i.e., feature descriptors in topological data analysis. PIFs can be calculated and compared in linear time and have many beneficial properties, such as the availability of a kernel-based similarity measure. We demonstrate their usage in common data analysis scenarios, such as confidence set estimation and classification of complex structured data.

math.AT↗