Related papers: Computing three-dimensional densities from force d…
While powerful methods have been developed for high-dimensional hypothesis testing assuming orthogonal parameters, current approaches struggle to generalize to the more common non-orthogonal case. We propose Stable Distillation (SD), a…
Generating geometric 3D reconstructions from Neural Radiance Fields (NeRFs) is of great interest. However, accurate and complete reconstructions based on the density values are challenging. The network output depends on input data, NeRF…
Despite being vastly ignored in the literature, coping with topological noise is an issue of increasing importance, especially as a consequence of the increasing number and diversity of 3D polygonal models that are captured by devices of…
We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…
Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach to derive effective…
Semantic correspondence, the task of determining relationships between different parts of images, underpins various applications including 3D reconstruction, image-to-image translation, object tracking, and visual place recognition. Recent…
Semantic scene completion, also known as semantic occupancy prediction, can provide dense geometric and semantic information for autonomous vehicles, which attracts the increasing attention of both academia and industry. Unfortunately,…
Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…
With systems for acquiring 3D surface data being evermore commonplace, it has become important to reliably extract specific shapes from the acquired data. In the presence of noise and occlusions, this can be done through the use of…
We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…
We model a microchannel cooling system and consider the optimization of its shape by means of shape calculus. A three-dimensional model covering all relevant physical effects and three reduced models are introduced. The latter are derived…
Molecular dynamics (MD) simulations are powerful tools for elucidating the macroscopic physical properties of materials from microscopic atomic behaviors. However, the massive, high-dimensional datasets generated by MD simulations pose a…
In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$,…
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…
The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high performance computing systems and/or accelerators. However, these systems…
We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore,…
The human cochlea is a remarkable device, able to discern extremely small amplitude sound pressure waves, and discriminate between very close frequencies. Simulation of the cochlea is computationally challenging due to its complex geometry,…
Three-dimensional molecular structure generation is typically performed at the level of individual atoms, yet molecular graph generation techniques often consider fragments as their structural units. Building on the advances in frame-based…
Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…
Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…