Related papers: When Locally Linear Embedding Hits Boundary

This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…

Several enhanced sampling techniques rely on the definition of collective variables to effectively explore free energy landscapes. Existing variables that describe the progression along a reactive pathway offer an elegant solution but face…

Among applications of deep learning (DL) involving low cost sensors, remote image classification involves a physical channel that separates edge sensors and cloud classifiers. Traditional DL models must be divided between an encoder for the…

We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…

The paper studies the local geometry of embedding clouds induced by \emph{controlled local classes of semantically close sentences}. The central question is how controlled paraphrase-like semantic variation is organized in sentence…

We present LBS-AE; a self-supervised autoencoding algorithm for fitting articulated mesh models to point clouds. As input, we take a sequence of point clouds to be registered as well as an artist-rigged mesh, i.e. a template mesh equipped…

Accurate modeling of complex physical problems, such as fluid-structure interaction, requires multiphysics coupling across the interface, which often has intricate geometry and dynamic boundaries. Conventional numerical methods face…

Traditional deep network training methods optimize a monolithic objective function jointly for all the components. This can lead to various inefficiencies in terms of potential parallelization. Local learning is an approach to…

The sensing process of large-scale LiDAR point clouds inevitably causes large blind spots, i.e. regions not visible to the sensor. We demonstrate how these inherent sampling properties can be effectively utilized for self-supervised…

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…

Exemplar-based methods rely on informative data points or prototypes to guide the optimization of learning algorithms. Such data facilitate interpretable model design and prediction. Of particular interest is the utility of exemplars in…

We consider the problem of reconstructing an embedding of a compact connected Riemannian manifold in a Euclidean space up to an almost isometry, given the information on intrinsic distances between points from its ``sufficiently large''…

The convergence problem of the Laplace-Beltrami operators plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve the operator. In this note…

In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows.…

Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from…

Knowing the link between observed predictive variables and outcomes is crucial for making inference in any regression model. When this link is missing, partially or completely, classical estimation methods fail in recovering the true…

In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and…

In this paper, we present a general approach to obtain numerical schemes with good mesh properties for problems with moving boundaries, that is for evolving submanifolds with boundaries. This includes moving domains and surfaces with…

Learning point clouds is challenging due to the lack of connectivity information, i.e., edges. Although existing edge-aware methods can improve the performance by modeling edges, how edges contribute to the improvement is unclear. In this…

Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To…