Abstract--Advancements in tools like Shapely 2.0 and Triton can significantly improve the efficiency of spatial similarity computations by enabling faster and more scalable geometric operations [1], [2]. However, for extremely large datasets, these optimizations may face challenges due to the sheer volume of computations required. T o address this, we propose a framework that reduces the number of clusters requiring verification, thereby decreasing the computational load on these systems. The framework integrates dynamic similarity index thresholding, supervised scheduling [3], and recall-constrained optimization to efficiently identify clusters with the highest spatial similarity while meeting user-defined precision and recall requirements [4]. By leveraging Kernel Density Estimation (KDE) to dynamically determine similarity thresholds [5] and machine learning models to prioritize clusters, our approach achieves substantial reductions in computational cost without sacrificing accuracy. Experimental results demonstrate the scalability and effectiveness of the method, offering a practical solution for large-scale geospatial analysis. Geospatial data constitutes the cornerstone of numerous applications across various domains, including urban planning, environmental monitoring, infrastructure development, and medicine. For example, OpenStreetMap contains global data amounting to over 1.5 terabytes [6], while GeoNames describes more than 12 million locations, providing extensive point geometries such as latitude and longitude [7]. Expanding these datasets, geospatial knowledge graphs like Y AGO2geo integrate millions of lines, polygons, and multi-polygons from OpenStreetMap and administrative divisions [8], while WorldKG represents around 113.4 million geographic entities [9]. KnowWhereGraph, a more recent initiative, comprises over 12 billion RDF triples, including data on polygons and multipolygons, and supports applications in disaster relief, agricultural land use, and food-related supply chains [10]. Even cross-domain knowledge graphs such as DBpedia and Wikidata incorporate a substantial amount of geospatial information, underscoring the critical role of spatial data on the Web. Beyond these well-known repositories, spatial datasets also play a transformative role in medicine, particularly in the analysis and modeling of organ structures. For instance, the Visible Human Project provides high-resolution spatial data for anatomical structures [11], while the Human Connectome Project captures detailed spatial relationships within the brain [12].

To address this, conditioning methods have been proposed, such as ControlNet [51] and IPadapter [48], that aim to capture the desired shape or form more explicitly through the use of edge or depth maps as input conditions. Despite these advancements, current text-and image-conditioned synthesis approaches still face a number of challenges. First, they often struggle to balance both textual and visual conditions, when text describes a particular context that should be combined with the target shape to guide an image synthesis (Figure 1, top row). Second, commonly used visual conditions such as edge or depth maps are limited to a single viewpoint, resulting in a loss of valuable 3D shape information when users seek image variations of an underlying shape from different poses. Third, even when these models accurately reflect the target shape in specific views, users may want to explore shape variations - yet current models often lack flexible controls for such exploration. To overcome these challenges, we propose ShapeWords, a method designed to generate images that faithfully adhere to both the text prompt and a target 3D shape geometry, 1 arXiv:2412.02912v1

For many scientific inverse problems we are required to evaluate an expensive forward model. Moreover, the model is often given in such a form that it is unrealistic to access its gradients. In such a scenario, standard Markov Chain Monte Carlo algorithms quickly become impractical, requiring a large number of serial model evaluations to converge on the target distribution. In this paper we introduce Flow Annealed Kalman Inversion (FAKI). This is a generalization of Ensemble Kalman Inversion (EKI), where we embed the Kalman filter updates in a temperature annealing scheme, and use normalizing flows (NF) to map the intermediate measures corresponding to each temperature level to the standard Gaussian. In doing so, we relax the Gaussian ansatz for the intermediate measures used in standard EKI, allowing us to achieve higher fidelity approximations to non-Gaussian targets. We demonstrate the performance of FAKI on two numerical benchmarks, showing dramatic improvements over standard EKI in terms of accuracy whilst accelerating its already rapid convergence properties (typically in $\mathcal{O}(10)$ steps).

We propose a data-driven optimization-based pre-compensation method to improve the contour tracking performance of precision motion stages by modifying the reference trajectory and without modifying any built-in low-level controllers. The position of the precision motion stage is predicted with data-driven models, a linear low-fidelity model is used to optimize traversal time, by changing the path velocity and acceleration profiles then a non-linear high-fidelity model is used to refine the previously found time-optimal solution. We experimentally demonstrate that the proposed method is capable of simultaneously improving the productivity and accuracy of a high precision motion stage. Given the data-based nature of the models, the proposed method can easily be adapted to a wide family of precision motion systems.

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture is used to learn the underlying physical behaviour of fluid flows. The network is used to infer the solution of flow simulations, which will be shown for a wide range of generic channel flow simulations. Physical meaningful quantities can be computed on the obtained solution, e.g. the total pressure difference or the forces on the objects. A Spatial Transformer Network with thin-plate-splines is used for the interaction between the physical constraints and the geometric representation of the objects. Thus, a transformation from an initial to a target geometry is performed such that the object is fulfilling the given constraints. This method is fully differentiable i.e., gradient informations can be used for the transformation. This can be seen as an inverse design process. The advantage of this method over many other proposed methods is, that the physical constraints are based on the inferred flow field solution. Thus, we have a transferable model which can be applied to varying problem setups and is not limited to a given set of geometry parameters or physical quantities.