Related papers: MetricGrids: Arbitrary Nonlinear Approximation wit…
We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/multiresolution method for PDEs with rough ($L^\infty$) coefficients with rigorous a-priori accuracy and performance estimates. The method is discovered…
Deep learning-based bilateral grid processing has emerged as a promising solution for image enhancement, inherently encoding spatial and intensity information while enabling efficient full-resolution processing through slicing operations.…
Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as…
Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to…
Recent years have seen substantial progress in neural generation of text, images, and audio, supported by mature training pipelines and large-scale optimization. For graphs, however, comparable progress has been more limited. We attribute…
In most existing learning systems, images are typically viewed as 2D pixel arrays. However, in another paradigm gaining popularity, a 2D image is represented as an implicit neural representation (INR) - an MLP that predicts an RGB pixel…
Reconstructing neural radiance fields with explicit volumetric representations, demonstrated by Plenoxels, has shown remarkable advantages on training and rendering efficiency, while grid-based representations typically induce considerable…
Network representation learning has traditionally been used to find lower dimensional vector representations of the nodes in a network. However, there are very important edge driven mining tasks of interest to the classical network analysis…
Recently Implicit Neural Representations (INRs) gained attention as a novel and effective representation for various data types. Thus far, prior work mostly focused on optimizing their reconstruction performance. This work investigates INRs…
Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper…
We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the…
In recent years, implicit online dense mapping methods have achieved high-quality reconstruction results, showcasing great potential in robotics, AR/VR, and digital twins applications. However, existing methods struggle with slow texture…
Traditionally, the geometric multigrid method is used with nested levels. However, the construction of a suitable hierarchy for very fine and unstructured grids is, in general, highly non-trivial. In this scenario, the non-nested multigrid…
Implicit neural representations (INRs) have recently emerged as a powerful tool that provides an accurate and resolution-independent encoding of data. Their robustness as general approximators has been shown in a wide variety of data…
In this paper, we develop a multigrid method on unstructured shape-regular grids. For a general shape-regular unstructured grid of ${\cal O}(N)$ elements, we present a construction of an auxiliary coarse grid hierarchy on which a geometric…
There are many ways to represent a molecule as input to a machine learning model and each is associated with loss and retention of certain kinds of information. In the interest of preserving three-dimensional spatial information, including…
The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…
This paper is concerned with fundamental limits on the approximation of nonlinear dynamical systems. Specifically, we show that recurrent neural networks (RNNs) can approximate nonlinear systems -- that satisfy a Lipschitz property and…
Encoding the distance between locations in space is essential for accurate navigation. Grid cells, a functional class of neurons in medial entorhinal cortex, are believed to support this computation. However, existing theories of how…
We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the prevailing issues around skeleton sparsity and reconstruction accuracy in existing skeletal representations. Our approach augments the continuous…