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3D Gaussian Splatting (3DGS) has recently enabled real-time photorealistic rendering in compact scenes, but scaling to large urban environments introduces severe aliasing artifacts and optimization instability, especially under…
Coarse-grained (CG) molecular dynamics (MD) simulations can simulate large molecular complexes over extended timescales by reducing degrees of freedom. A critical step in CG modeling is the selection of the CG mapping algorithm, which…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
We consider the problem of matrix completion with graphs as side information depicting the interrelations between variables. The key challenge lies in leveraging the similarity structure of the graph to enhance matrix recovery. Existing…
Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and…
A Generative Adversarial Network (GAN) with generator $G$ trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. Here, we propose a new method of deploying a…
Decentralized and asynchronous communications are two popular techniques to speedup communication complexity of distributed machine learning, by respectively removing the dependency over a central orchestrator and the need for…
$\textbf{Graph Coarsening (GC)}$ is a prominent graph reduction technique that compresses large graphs to enable efficient learning and inference. However, existing GC methods generate only one coarsened graph per run and must recompute…
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive,…
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations…
Quantum unitaries of the form $\Sigma_{c}\ket{c}\bra{c}\otimes U_{c}$ are ubiquitous in quantum algorithms. This class encompasses not only standard uniformly controlled gates (UCGs) but also a wide range of circuits with uniformly…
In this paper we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [5] which used the geometric structure of optimal transport to introduce the conceptual basis…
The arithmetic mean/geometric mean-inequality (AM/GM-inequality) facilitates classes of non-negativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic…
We consider the solution of elliptic problems on the tensor product of two physical domains as e.g. present in the approximation of the solution covariance of elliptic partial differential equations with random input. Previous sparse…
The traditional Triangular Maximally Filtered Graph (TMFG) construction requires pre-computation and storage of a dense correlation matrix; this limits its applicability to small and medium-sized datasets. Here we identify key memory and…
Cardiac magnetic resonance imaging (CMR) is vital for diagnosing heart diseases, but long scan time remains a major drawback. To address this, accelerated imaging techniques have been introduced by undersampling k-space, which reduces the…
Simultaneous localization and mapping (SLAM) is a critical capability in autonomous navigation, but memory and computational limits make long-term application of common SLAM techniques impractical; a robot must be able to determine what…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
Coarse-Graining (CG) models are low resolution approximation of high resolution models, such as all-atomic (AA) models. An effective CG model is expected to reproduce equilibrium values of sufficient physical quantities of its AA model,…
Cartesian-grid methods with Adaptive Mesh Refinement (AMR) are ideally suited for simulating the breaking of waves, the formation of spray, and the entrainment of air around ships. As a result of the cartesian-grid formulation, minimal…