Mgr. Vojtěch Rybář

Mgr. Vojtěch Rybář

Ing. Daniel Vašata, Ph.D.

Department of Applied Mathematics

This paper includes research in the field of cleaning and filling in datasets and focuses on a specific approach using probabilistic programming. The practical part of the work operates with the probabilistic programming language PClean, programmed in Julia. The principles on which it operates are explained and the specific parts required to write the program are laid out. Subsequently, PClean is used to write a program for filling and correcting values in a data set with car records (price, power, fuel, etc.) Once this dataset is corrected, regression is used to estimate the price and the quality of the result is compared with the results based on uncorrected data with standardised added values for each column or added based on expert knowledge. The model learned the data via PClean does not achieve the qualities of the model based on expert knowledge. However, PClean does offer a fast way to fill in missing categorical values with a quality exceeding the trivial fill-in mechanism commonly used today.

Thesis on DSpace

Mgr. Vojtěch Rybář

Ing. Daniel Vašata, Ph.D.

Department of Applied Mathematics

In this thesis we reviewed uses of machine learning in computational fluid dynamics. We then implemented a state-of-the-art graph neural network to simulate the flow around an airfoil in 2D. We train the model at lower speeds and angles of attack and then extrapolate to higher ones. We trained a model that extrapolates with a small precision error and remains stable on long rollouts.

Thesis on DSpace

Mgr. Vojtěch Rybář

Ing. Magda Friedjungová, Ph.D.

Department of Applied Mathematics

Machine Learning is becoming more and more used in many sensitive applications where it is essential to understand why the models behave as they do. Such a rapid increase has heightened the demand for Explainable Machine Learning and new explanation methods. These methods, however, are not guaranteed to yield consistent outputs. This work give a concise overview of the current state of Explainable Machine Learning and its methods, focusing primarily on the local explanation methods (e.g. SHAP and LIME) and global plotting methods for tabular data, and methods specific to neural network models. We show examples of inconsistent explanations of SHAP and LIME, illustrate and explain how some methods are impacted by correlation, and show practical examples of using neural network methods to analyze the model and find its biases. In the end we give some recommendations when dealing with inconsistent outputs based on the research we made and our own experiments.

Thesis on DSpace

Mgr. Vojtěch Rybář

Ing. Daniel Vašata, Ph.D.

Department of Applied Mathematics

This thesis provides a detailed examination of the Vision Transformer (ViT) architecture and the explainability methods available for this architecture. The theoretical section thoroughly analyses the structure and operational principles of ViT and the attention mechanism. Additionally, the theoretical part reviews the current state of explainability methods for ViT, exploring the fundamentals of their functioning, their classifications, and the metrics used to compare their properties. The practical section focuses on evaluating three explainability methods: Beyond Intuition, GradientExplainer, and ViT-Shapley. These methods were applied to PyTorch ViT models that were pre-trained on the ImageNet21K dataset and subsequently fine-tuned on training data from two datasets. The experiments examined the characteristics of these methods, such as faithfulness, robustness, and complexity, using several metrics.

Thesis on DSpace

Mgr. Vojtěch Rybář

Ing. Ivo Petr, Ph.D.

Department of Applied Mathematics

The main objective of this thesis is to provide further proof that interpretable models can achieve similar, if not better performance than black-box models. In our experiment, we found that there was not one dataset, where the black-box model performed significantly better than its interpretable counterparts, the highest difference we saw in terms of the F1 score was 0.02. This advantage is definitely not significant enough to outweigh the advantages brought about by an inherently interpretable model. This is especially true for high-stakes decisions, where we would be forced to use an explainability method, which could fail to reveal bias in the black-box model, potentially leading to poor performance in the real world.

Thesis on DSpace

Mgr. Vojtěch Rybář

Dr. Rodrigo Augusto da Silva Alves

Department of Applied Mathematics

Predictive maintenance of cars is primarily focused on forecasting failures of specific components using internal sensor data. This thesis explores the feasibility of using historical repair shop data for predictive maintenance of vehicles. The broad scope of the repair data allows us to predict failures of various components across the entire vehicle. We present three modeling approaches for predictive maintenance. First, we use regression to forecast the remaining useful life of different car components. Second, we apply classification to predict future repairs over varying prediction horizons. Third, we model the data as a next-basket recommendation task, predicting a set of likely repair items. In all three approaches, we achieve consistent improvements over baseline models. Our results demonstrate the potential of using real-world repair data for predictive maintenance, optimizing cost-effectiveness, and minimizing inconvenience and waste for both businesses and drivers.

Mgr. Vojtěch Rybář

Ing. Miroslav Čepek, Ph.D.

Department of Applied Mathematics

The European electricity grid is a complex, interconnected system that spans multiple countries and supports cross-border energy trade. Accurate forecasting of electricity flows is essential for maintaining grid stability and optimizing trading strategies. This thesis investigates the application of Graph Neural Networks (GNNs), specifically Message Passing Neural Networks (MPNNs), for predicting day-ahead electricity flows across European bidding zones. The study incorporates proprietary and open-source datasets, capturing renewable generation forecasts, residual loads, and market indicators such as temperature and fuel prices. Three model variants were developed and evaluated: a baseline MPNN, a Monte Carlo Dropout model, and a Bayesian Neural Network with uncertainty quantification. Experimental results indicate that while the baseline model achieved the highest predictive accuracy, uncertainty-aware models offered valuable confidence intervals, albeit with challenges in calibration. Performance analysis across borders and time of day revealed key sources of error related to renewable volatility and regional flow volumes. These findings demonstrate the potential of GNNs for grid modeling and highlight areas for future improvement, including ensemble diversity and real-time adaptability.