相关论文: A Statistical Approach to Surface Metrology for 3D…

Context: Software metrics, as one form of static analyses, is a commonly used approach in software engineering in order to understand the state of a software system, in particular to identify potential areas prone to defects. Family-based…

Traditional member-based two-step design approaches included in current structural codes for steel structures, as well as more recent system-based direct-design alternatives, require building rigorous structural reliability frameworks for…

Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…

In the era of big data, integrating multi-source functional data to extract a subspace that captures the shared subspace across sources has attracted considerable attention. In practice, data collection procedures often follow…

3D scene modeling techniques serve as the bedrocks in the geospatial engineering and computer science, which drives many applications ranging from automated driving, terrain mapping, navigation, virtual, augmented, mixed, and extended…

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…

We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary…

There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…

Nanoscale design of surfaces and interfaces is essential for modern technologies like organic LEDs, batteries, fuel cells, superlubricating surfaces, and heterogeneous catalysis. However, these systems often exhibit complex surface…

The latest sheet stamping processes enable efficient manufacturing of complex shape structural components that have high stiffness to weight ratios, but these processes can introduce defects. To assist component design for stamping…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…

Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…

After the recent ground-breaking advances in protein structure prediction, one of the remaining challenges in protein machine learning is to reliably predict distributions of structural states. Parametric models of fluctuations are…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one-forms. We provide a numerical framework for the computation…

Graph-based machine learning has emerged as a promising approach for manufacturability analysis by learning directly from CAD models represented as Boundary Representations (B-reps), exploiting both surface geometry and topological…

Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…