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Projecting the ice sheets' contribution to sea-level rise is difficult because of the complexity of accurately modeling ice sheet dynamics for the full polar ice sheets, because of the uncertainty in key, unobservable parameters governing those dynamics, and because quantifying the uncertainty in projections is necessary when determining the confidence to place in them. This work presents the formulation and solution of the Bayesian inverse problem of inferring, from observations, a probability distribution for the basal sliding parameter field beneath the Antarctic ice sheet. The basal sliding parameter is used within a high-fidelity nonlinear Stokes model of ice sheet dynamics. This model maps the parameters "forward" onto a velocity field that is compared against observations. Due to the continental-scale of the model, both the parameter field and the state variables of the forward problem have a large number of degrees of freedom: we consider discretizations in which the parameter has more than 1 million degrees of freedom. The Bayesian inverse problem is thus to characterize an implicitly defined distribution in a high-dimensional space. This is a computationally demanding problem that requires scalable and efficient numerical methods be used throughout: in discretizing the forward model; in solving the resulting nonlinear equations; in solving the Bayesian inverse problem; and in propagating the uncertainty encoded in the posterior distribution of the inverse problem forward onto important quantities of interest. To address discretization, a hybrid parallel adaptive mesh refinement format is designed and implemented for ice sheets that is suited to the large width-to-height aspect ratios of the polar ice sheets. An efficient solver for the nonlinear Stokes equations is designed for high-order, stable, mixed finite-element discretizations on these adaptively refined meshes. A Gaussian approximation of the posterior distribution of parameters is defined, whose mean and covariance can be efficiently and scalably computed using adjoint-based methods from PDE-constrained optimization. Using a low-rank approximation of the covariance of this distribution, the covariance of the parameter is pushed forward onto quantities of interest.

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Many autonomous robots operating in unknown and unstructured environments rely on building a dense 3D map of it during exploration. What tasks the robot can perform depends on the information stored in this map. Most 3D maps currently in use store information required for robot control and environment reconstruction – is this point in space occupied, or safe to navigate to? To enable more complex tasks additional information is required. We introduce Semantic UFOMap, an open-source octree based mapping framework designed for online use on limited hardware. Capable of real-time fusion and querying of semantic instances into the map – enabling high-level robot tasks and human-robot interaction. The online capabilities are evaluated using ground-truth data, where we show competitive results compared to voxel hashing, with optimizations still available. Additionally, we demonstrate a potential application with a simulated autonomous exploration and object navigation experiment. The evaluation shows that Semantic UFOMap is capable of real-time online performance. Storing semantic information in the map has the potential to open up new autonomous robot applications and yield improvements in existing tasks. / Autonoma robotar som opererar i okända och ostrukturerade mijöer är ofta beroende av att skapa en 3D-karta under utforskning av området. Villka uppgifter roboten kan utföra beror på informationen som finns tillgänglig i kartan. De flesta nuvarande kartor som används sparar information som behövs för säker navigation och miljörekonstruktion – är den här positionen ett hinder, eller är den säker att navigera till? För att möjligjöra mer komplexa uppgifter behöver roboten ha tillgång till ytterligare information. Vi presenterar Semantic UFOMap, ett öppen källkods kartläggnings ramverk för realtids användning på begränsad hårdvara. Genom att klara av realtids integrering och sökning av semantiska instanser i kartan möjliggör ramverket mer komplexa uppgifter och öppnar upp fler användningsområden i människa-robot interaktion. Utvärdering görs med hjälp av inspelad data, vi visar konkurrenskraftiga resultat jämfört med voxel hashning, med optimering fortfarande tillgänglig. Ett användningsområde demonstreras med ett simulerat autonomt utforsknings och objektnavigerings experiment. Utvärderingen visar att Semantic UFOMap klarar av realtids applikationer. Att spara semantisk information i kartan har potential att öppna upp för nya användningsområden inom robotik och leda till förbättringar i befintliga uppgifter.