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The problem of 3D object recognition is of immense practical importance, with the last decade witnessing a number of breakthroughs in the state of the art. Most of the previous work has focused on the matching of textured objects using…
Detailed analysis of scanning probe microscopy (SPM) data acquired for faceted and non-flat surfaces is usually complicated due to the presence of a large number of surface areas tilted by large/variable angles relative to the scanning…
In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…
In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…
Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…
Obtaining high quality particle distribution representing clean geometry in pre-processing is essential for the simulation accuracy of the particle-based methods. In this paper, several level-set based techniques for cleaning up `dirty'…
In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas-liquid two-phase flows through geometrical variables. The con- tribution is two-fold. First it participates in the…
Geofences have attracted significant attention in the design of spatial and virtual regions for managing and engaging spatiotemporal events. By using geofences to monitor human activity across their boundaries, content providers can create…
Geophysical model domains typically contain irregular, complex fractal-like boundaries and physical processes that act over a wide range of scales. Constructing geographically constrained boundary-conforming spatial discretizations of these…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing the orientations and shapes, respectively, of geological reflecting surfaces. Commonly, the…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
Surface meshes are widely used shape representations and capture finer geometry data than point clouds or volumetric grids, but are challenging to apply CNNs directly due to their non-Euclidean structure. We use parallel frames on surface…
Airborne magnetic data are commonly used to produce preliminary geological maps. Machine learning has the potential to partly fulfill this task rapidly and objectively, as geological mapping is comparable to a semantic segmentation problem.…