Physics-Informed Neural Networks (PINNs) are hybrid models that incorporate differential equations into the training of neural networks, with the aim of bringing the best of both worlds. This project used a mathematical model describing a Continuous Stirred-Tank Reactor (CSTR), to test two possible applications of PINNs. The first type of PINN was trained to predict an unknown reaction rate law, based only on the differential equation and a time series of the reactor state. The resulting model was used inside a multi-step solver to simulate the system state over time. The results showed that the PINN could accurately model the behaviour of the missing physics also for new initial conditions. However, the model suffered from extrapolation error when tested on a larger reactor, with a much lower reaction rate. Comparisons between using a numerical derivative or automatic differentiation in the loss equation, indicated that the latter had a higher robustness to noise. Thus, it is likely the best choice for real applications. A second type of PINN was trained to forecast the system state one-step-ahead based on previous states and other known model parameters. An ordinary feed-forward neural network with an equal architecture was used as baseline. The second type of PINN did not outperform the baseline network. Further studies are needed to conclude if or when physics-informed loss should be used in autoregressive applications.

During production of certain biopharamaceutical drugs, cells are grown in a liquid mediainside bioreactors with the goal of producing a specic biomaterial that can be rened intoa drug. This project investigates whether the use of Neural Networks (NN) can decreasethe prediction error, in terms of Mean Squared Error (MSE), for 2 metabolic processes incells compared to current methods. The rst experiment tests predictions of cell-SpecicConsumption Rate (SCR) of 5 dierent metabolites and the second experiment testspredictions of cell-Specic Production Rate (SPR) of titer. Fully connected feed-forwardneural networks were trained and cross-validation was used to obtain MSE betweenpredictions and measured values. The SCR predictions made by the NN was better thanthe original model predictions for all 5 metabolites. The predictions of SPR from the NNcannot with certainty be said to be better than the original model, with a p-value of 0.13.These results indicate that using NNs when modeling cell metabolism in bioreactors candecrease its prediction error, leading to better control of the bioreactor environment andmore ecient production.

Today new drugs are tested on cell cultures in wells to minimize time, cost, andanimal testing. The cells are studied using microscopy in different ways and fluorescentprobes are used to study finer details than the light microscopy can observe.This is an invasive method, so instead of molecular analysis, imaging can be used.In this project, phase-contrast microscopy images of cells together with fluorescentmicroscopy images were used. We use Machine Learning to predict the fluorescentimages from the light microscopy images using a strategy called In-Silico Labeling.A Convolutional Neural Network called U-Net was trained and showed good resultson two different datasets. Pixel-wise regression, pixel-wise classification, andimage classification with one cell in each image was tested. The image classificationwas the most difficult part due to difficulties assigning good quality labels tosingle cells. Pixel-wise regression showed the best result.

(English) This study has two aims. First, to reconstruct the landscape arrangement of the northern tip of the North Bohemian Basin at the end of the baroque era, focusing on compositional relationships between landscape dominants, both in a scale of pilgrim areas, castles, churches and monasteries and in a scale of chapels and small sculptural and architectonic monuments. The second aim is to, on the example of this - in baroque era extraordinarily rich landscape - examine the phenomenon of the Czech baroque landscape by comparing conclusions of the reconstruction with the widespread conception of compositional principles of baroque landscape. For this purpose, a comprehensive catalogue of architectonic and sculptural monuments in the researched area at about 1780, was compiled. Thereafter a map was created, that shows not only the objects as such, but also the compositional relationships between them. The most important resource for the map was a collection of maps of the First military mapping of Bohemia. In the text, the landscape is described through the perspective of a baroque pilgrim, browsing the landscape along the old roads of three selected routes. The conclusions are then summarized in the final chapter. As a result of my study, I came to the conclusion, that neither the researched...