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Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are…

Deep learning models with a large number of parameters, often referred to as over-parameterized models, have achieved exceptional performance across various tasks. Despite concerns about overfitting, these models frequently generalize well…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Point clouds have grown in importance in the way computers perceive the world. From LIDAR sensors in autonomous cars and drones to the time of flight and stereo vision systems in our phones, point clouds are everywhere. Despite their…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries…

While several convolution-like operators have recently been proposed for extracting features out of point clouds, down-sampling an unordered point cloud in a deep neural network has not been rigorously studied. Existing methods down-sample…

Developing fast regression models (surrogate/metamodels) from DEM data is key for practical industrial application to allow real-time evaluations. However, benchmarking different models is often overlooked in particle technology for…

This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated…

In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…

Recent years have witnessed the growth of point cloud based applications because of its realistic and fine-grained representation of 3D objects and scenes. However, it is a challenging problem to compress sparse, unstructured, and…

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…

This paper proposes a lossless point cloud (PC) geometry compression method that uses neural networks to estimate the probability distribution of voxel occupancy. First, to take into account the PC sparsity, our method adaptively partitions…

Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data…

Point cloud is often regarded as a discrete sampling of Riemannian manifold and plays a pivotal role in the 3D image interpretation. Particularly, rotation perturbation, an unexpected small change in rotation caused by various factors (like…

We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…

In recent years, point cloud generation has gained significant attention in 3D generative modeling. Among existing approaches, point-based methods directly generate point clouds without relying on other representations such as latent…

We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs,…

Material extrusion is one of the most commonly used approaches within the additive manufacturing processes available. Despite its popularity and related technical advancements, process reliability and quality assurance remain only partially…