This thesis presents results on the theoretical description of ion acceleration using ultra-short ultra-intense laser pulses. It consists of two parts. One deals with the very general and underlying description and theoretic modeling of the laser interaction with the plasma, the other part presents three approaches of optimizing the ion acceleration by target geometry improvements using the results of the first part. In the first part, a novel approach of modeling the electron average energy of an over-critical plasma that is irradiated by a few tens of femtoseconds laser pulse with relativistic intensity is introduced. The first step is the derivation of a general expression of the distribution of accelerated electrons in the laboratory time frame. As is shown, the distribution is homogeneous in the proper time of the accelerated electrons, provided they are at rest and distributed uniformly initially. The average hot electron energy can then be derived in a second step from a weighted average of the single electron energy evolution. This result is applied exemplary for the two important cases of infinite laser contrast and square laser temporal profile, and the case of an experimentally more realistic case of a laser pulse with a temporal profile sufficient to produce a preplasma profile with a scale length of a few hundred nanometers prior to the laser pulse peak. The thus derived electron temperatures are in excellent agreement with recent measurements and simulations, and in particular provide an analytic explanation for the reduced temperatures seen both in experiments and simulations compared to the widely used ponderomotive energy scaling. The implications of this new electron temperature scaling on the ion acceleration, i.e. the maximum proton energy, are then briefly studied in the frame of an isothermal 1D expansion model. Based on this model, two distinct regions of laser pulse duration are identified with respect to the maximum energy scaling. For short laser pulses, compared to a reference time, the maximum ion energy is found to scale linearly with the laser intensity for a simple flat foil, and the most important other parameter is the laser absorption efficiency. In particular the electron temperature is of minor importance. For long laser pulse durations the maximum ion energy scales only proportional to the square root of the laser peak intensity and the electron temperature has a large impact. Consequently, improvements of the ion acceleration beyond the simple flat foil target maximum energies should focus on the increase of the laser absorption in the first case and the increase of the hot electron temperature in the latter case. In the second part, exemplary geometric designs are studied by means of simulations and analytic discussions with respect to their capability for an improvement of the laser absorption efficiency and temperature increase. First, a stack of several foils spaced by a few hundred nanometers is proposed and it is shown that the laser energy absorption for short pulses and therefore the maximum proton energy can be significantly increased. Secondly, mass limited targets, i.e. thin foils with a finite lateral extension, are studied with respect to the increase of the hot electron temperature. An analytical model is provided predicting this temperature based on the lateral foil width. Finally, the important case of bent foils with attached flat top is analyzed. This target geometry resembles hollow cone targets with flat top attached to the tip, as were used in a recent experiment producing world record proton energies. The presented analysis explains the observed increase in proton energy with a new electron acceleration mechanism, the direct acceleration of surface confined electrons by the laser light. This mechanism occurs when the laser is aligned tangentially to the curved cone wall and the laser phase co-moves with the energetic electrons. The resulting electron average energy can exceed the energies from normal or oblique laser incidence by several times. Proton energies are therefore also greatly increased and show a theoretical scaling proportional to the laser intensity, even for long laser pulses.

This thesis investigates the use of sampled CAD models for training and calibrating a semantic segmentation model, RandLA-Net, with the ultimate goal of localizing modules for digital twinning (the process of creating digital twins). A significant contribution is the development of the Random Placement of Component Generator (RPCG), a synthetic dataset generator that randomly places CAD models within scenes while preserving contextual information such as typical height above ground. Training and testing on datasets generated by RPCG demonstrated its ability to recognize class modules in various randomly generated scenes. Various hyperparameters related to the loss function and pre-processing steps were explored to improve RandLA-Net’s generalization to different contextual settings. Notably, using a class-weighted α in the focal loss showed promise in correctly classifying infrequent classes and reducing network overconfidence under domain shifts with similar prior probability distributions. The semantic segmentation results were promising for the RPCG test set, achieving a mean True Positive Rate (mTPR) of 98% and a mean Intersection over Union(mIoU) of 93.6%. However, the performance on a sampled version of a CAD model representing an installation named Undercentral was comparatively lower, with a mTPR of 41.1% and a mIoU of 33.4%, indicating the need for further adaptation to varied contextual environments. Proposed improvements include enhancing RPCG with an occupancy grid to better simulate compact scenes and evaluating different subsampling rates in RandLA-Net’s random sampling layers. For confidence calibration, the thesis finds that averaging multiple Monte Carlo (MC) dropout evaluations effectively reduces network overconfidence and improves model reliability. Although this work addresses only a portion of the overall digital twinning process, it highlights the potential of synthetic data generation in enhancing semantic segmentation models and contributes towards the localization of modules in digital twin creation.

This thesis investigates predicting the Intersection over Union (IoU) in detections made by the face detector YOLO5Face, which is done to use the predicted IoU as a new uncertainty measure. The detections are done on the face dataset WIDER FACE, and the prediction of IoU is made by adding a parallel head to the existing YOLO5Face architecture. Experiments show that the methodology for predicting the IoU used in this thesis does not work and the parallel prediction head fails to predict the IoU and instead resorts to predicting common IoU values. The localisation confidence and classification confidences of YOLO5Face are then investigated to find out which confidence measure is least uncertain and most suitable to use when identifying faces. Experiments show that the localisation confidence is consistently more calibrated than the classification confidence. The classification confidence is then calibrated with respect to the localisation confidence which reduces the Expected Calibration Error (ECE) for classification confidence from 0.17 to 0.01.