Gravity is the main driving force for groundwater flow, and both landscape topography and geology distribute the effects of gravity on groundwater flow.  The groundwater table defines the distribution of the potential energy of the water. In humid regions where the bedrock permeability is relatively low and the soil depth is sufficiently shallow, the groundwater table closely follows the landscape topography and, thus, the topography controls the groundwater circulation in these regions. In this thesis, I investigate multi-scale topography-controlled groundwater flow, with the goal of systematizing the spatial distribution of groundwater flow and assessing geological parameters of importance for groundwater circulation.  Both exact solutions and numerical models are utilized for analyzing topography-controlled groundwater flow. The more complex numerical models are used to explore the importance of various simplifications of the exact solutions. The exact solutions are based on spectral representation of the topography and superpositioning of unit solutions to the groundwater flow field. This approach is an efficient way to analyze multi-scaled topography-controlled groundwater flow because the impact of individual topographic scales on the groundwater flow can be analyzed separately.  The results presented here indicate that topography is fractal and affects groundwater flow cells at wide range of spatial scales. We show that the fractal nature of the land surface produces fractal distributions of the subsurface flow patterns. This underlying similarity in hydrological processes also yields a single scale-independent distribution of subsurface water residence times which have been found in distributions of solute efflux from watersheds. Geological trends modify the topographic control of the groundwater circulation pattern and this thesis presents exact solutions explaining the impact of geological layering, depth-decaying and anisotropic hydraulic conductivity on the groundwater flow field. For instance, layers of Quaternary deposits and decaying permeability with depth both increase the importance of smaller topographic scales and creates groundwater flow fields where a larger portion of the water occupies smaller and shallower circulation cells, in comparison to homogeneous systems. / Gravitationen är den mest betydelsefulla drivkraften för grundvattenströmning. Topografin och geologin fördelar vattnets potentiella energi i landskapet. Grundvattenytans läge definierar vattnets potentiella energi, vilket är ett randvillkor för grundvattnets strömningsfält. I humida områden med en relativt tät berggrund och tillräckligt tunna jordlager, följer grundvattenytan landskapets topografi. Därav följer att grundvattenströmningen är styrd av topografin i dessa områden. I denna avhandling belyser jag den flerskaliga topografistyrda grundvattenströmningen. Min målsättning har varit att kvantitativt bestämma grundvattenströmningens rumsliga fördelning samt att undersöka hur olika geologiska parametrar påverkar grundvattencirkulationen. Jag har använt såväl numeriska modeller som analytiska lösningar, för att undersöka hur topografin styr grundvattenströmningen. De numeriska modellerna är mer komplexa än de analytiska lösningarna och kan därför användas för att undersöka betydelserna av olika förenklingar som finns i de analytiska lösningarna. De analytiska lösningarna är baserade på spektralanalys av topografin, samt superponering av enhetslösningar, där varje enhetslösning beskriver hur en specifik topografisk skala påverkar grundvattnets strömningsfält. Detta är ett effektivt tillvägagångssätt för att undersöka flerskaliga effekter av topografin, eftersom påverkan av varje enskild topografisk skala kan studeras separat. Resultaten som presenteras indikerar att topografin är fraktal och att den ger upphov till cirkulationsceller av varierande storlek som även dessa är av en fraktal natur. Denna grundläggande fördelning i grundvattnets strömningsfält ger upphov till att grundvattnets uppehållstid i marken följer ett självlikformigt mönster och kan förklara uppmätta tidsvariationer av lösta ämnens koncentrationer i vattendrag efter regn. Geologiska trender påverkar hur grundvattenströmningen styrs av topografin. De exakta lösningar som presenteras här, beskriver hur geologiska lager samt djupavtagande och anisotropisk hydraulisk konduktivitet påvekar grundvattnets strömning. Exempelvis är betydelsen av mindre topografiska skalor viktigare i områden med kvartära avlagringar och en berggrund med djupavtagande konduktivitet, än i områden med homogen bergrund utan kvartära avlagringar. Dessutom är en större andel strömmande vatten belägen närmare markytan i de förstnämnda områdena. / QC 20100802

This thesis explores using multi-scale topology optimization (TO) by utilizing inverse homogenization to automate the adjustment of each unit-cell's geometry and placement in a lattice structure within a pressure vessel (the design domain) to achieve desired structural properties. The aim is to find the optimal material distribution within the design domain as well as desired material properties at each discretized element and use machine learning (ML) to map microstructures with corresponding prescribed effective properties. Effective properties are obtained through homogenization, where microscopic properties are upscaled to macroscopic ones. The symmetry group of a unit-cell's elasticity tensor can be utilized for stiffness directional tunability, i.e., to tune the cell's performance in different load directions.  A few geometrical variations of a chosen unit-cell were homogenized to build an effective anisotropic elastic material model by obtaining their effective elasticity. The symmetry group and the stiffness directionality of the cells’ effective elasticity tensors were identified. This was done using both the pattern of the matrix representation of the effective elasticity tensor and the roots of the monoclinic distance function. A cell library of symmetry-preserving variations with a corresponding material property space was created, displaying the achievable properties within the library. Two ML models were implemented to map material properties to appropriate cells. A TO algorithm was also implemented to produce an optimal material distribution within a design domain of a pressure vessel in 2D to maximize stiffness. However, the TO algorithm to obtain desired material properties for each element in the domain was not realized within the time frame of this thesis.  The cells were successfully homogenized. The effective elasticity tensor of the chosen cell was found to belong to the cubic symmetry group in its natural coordinate system. The results suggest that the symmetry group of an elasticity tensor retrieved through numerical experiments can be identified using the monoclinic distance function. If near-zero minima are present, they can be utilized to find the natural coordinate system. The cubic symmetry allowed the cell library's material property space to be spanned by only three elastic constants, derived from the elasticity matrix. The orthotropic symmetry group can enable a greater directional tunability and design flexibility than the cubic one. However, materials exhibiting cubic symmetry can be described by fewer material properties, limiting the property space, which could make the multi-scale TO less complex. The ML models successfully predicted the cell parameters for given elastic constants with satisfactory results. The TO algorithm was successfully implemented. Two different boundary condition cases were used – fixing the domain’s corner nodes and fixing the middle element’s nodes. The latter was found to produce more sensible results. The formation of a cylindrical outer shape could be distinguished in the produced material design, which was deemed reasonable since cylindrical pressure vessels are consistent with engineering practice due to their inherent ability to evenly distribute load. The TO algorithm must be extended to include the elastic constants as design variables to enable the multi-scale TO.

Autonomous driving technology has the potential to revolutionize the way we think about transportation and its impact on society. Perceiving the environment is a key aspect of autonomous driving, which involves multiple computer vision tasks. Multi-scale deep learning has dramatically improved the performance on many computer vision tasks, but its practical use in autonomous driving is limited by the available resources in embedded systems. Multi-task learning offers a solution to this problem by allowing more compact deep learning models that share parameters between tasks. However, not all tasks benefit from being learned together. One way of avoiding task interference during training is to learn tasks in sequence, with each task providing useful information for the next – a scheme which builds on transfer learning. Multi-task and transfer dynamics are both concerned with the relationships between tasks, but have previously only been studied separately. This Master’s thesis investigates how different computer vision tasks relate to each other in the context of multi-task and transfer learning, using a state-ofthe-art efficient multi-scale deep learning model. Through an experimental research methodology, the performance on semantic segmentation, depth estimation, and object detection were evaluated on the Virtual KITTI 2 dataset in a multi-task and transfer learning setting. In addition, transfer learning with a frozen encoder was compared to constrained encoder fine tuning, to uncover the effects of fine-tuning on task dynamics. The results suggest that findings from previous work regarding semantic segmentation and depth estimation in multi-task learning generalize to multi-scale learning on autonomous driving data. Further, no statistically significant correlation was found between multitask learning dynamics and transfer learning dynamics. An analysis of the results from transfer learning indicate that some tasks might be more sensitive to fine-tuning than others, suggesting that transferring with a frozen encoder only captures a subset of the complexities involved in transfer relationships. Regarding object detection, it is observed to negatively impact the performance on other tasks during multi-task learning, but might be a valuable task to transfer from due to lower annotation costs. Possible avenues for future work include applying the used methodology to real-world datasets and exploring ways of utilizing the presented findings for more efficient perception algorithms. / Självkörande teknik har potential att revolutionera transport och dess påverkan på samhället. Självkörning medför ett flertal uppgifter inom datorseende, som bäst löses med djupa neurala nätverk som lär sig att tolka bilder på flera olika skalor. Begränsningar i mobil hårdvara kräver dock att tekniker som multiuppgifts- och sekventiell inlärning används för att minska neurala nätverkets fotavtryck, där sekventiell inlärning bygger på överföringsinlärning. Dynamiken bakom både multiuppgiftsinlärning och överföringsinlärning kan till stor del krediteras relationen mellan olika uppdrag. Tidigare studier har dock bara undersökt dessa dynamiker var för sig. Detta examensarbete undersöker relationen mellan olika uppdrag inom datorseende från perspektivet av både multiuppgifts- och överföringsinlärning. En experimentell forskningsmetodik användes för att jämföra och undersöka tre uppgifter inom datorseende på datasetet Virtual KITTI 2. Resultaten stärker tidigare forskning och föreslår att tidigare fynd kan generaliseras till flerskaliga nätverk och data för självkörning. Resultaten visar inte på någon signifikant korrelation mellan multiuppgift- och överföringsdynamik. Slutligen antyder resultaten att vissa uppgiftspar ställer högre krav än andra på att nätverket anpassas efter överföring.