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In recent years, molecular dynamics (MD) simulations have emerged as a pivotal tool for understanding the structure, dynamics, and phase behavior in charged soft matter systems. To explore phenomena across greater length and time scales in…
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian…
In this paper, we present a novel geometry-aware RGB-D Gaussian Splatting SLAM system, named G2S-ICP SLAM. The proposed method performs high-fidelity 3D reconstruction and robust camera pose tracking in real-time by representing each scene…
Recently, 3D Gaussian Splatting (3DGS), an explicit scene representation technique, has shown significant promise for dynamic novel-view synthesis from monocular video input. However, purely data-driven 3DGS often struggles to capture the…
Large scale Gaussian process (GP) regression is infeasible for larger data sets due to cubic scaling of flops and quadratic storage involved in working with covariance matrices. Remedies in recent literature focus on divide-and-conquer,…
3D Gaussian splats have emerged as a revolutionary, effective, learned representation for static 3D scenes. In this work, we explore using 2D Gaussian splats as a new primitive for representing videos. We propose GSVC, an approach to…
In this paper, we discuss an extension of the Split Hamiltonian Monte Carlo (Split HMC) method for Gaussian process model (GPM). This method is based on splitting the Hamiltonian in a way that allows much of the movement around the state…
Recent progress in compressing explicit radiance field representations, particularly 3D Gaussian Splatting, has substantially reduced memory consumption while improving real-time rendering performance. However, existing approaches remain…
We introduce an algorithm based on Generalized Dual Method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that…
Common time-explicit numerical methods for kinetic simulations of plasmas in the low-collisions limit fall into two classes of algorithms: momentum conserving and energy conserving. Each has certain drawbacks. The PIC algorithm does not…
Point clouds are a popular representation for 3D shapes. However, they encode a particular sampling without accounting for shape priors or non-local information. We advocate for the use of a hierarchical Gaussian mixture model (hGMM), which…
Molecular dynamics facilitates the simulation of a complex system to be analyzed at molecular and atomic levels. Simulations can last a long period of time, even months. Due to this cause the graphics processing units (GPUs) and multi-core…
The advent of 3D Gaussian Splatting (3D-GS) techniques and their dynamic scene modeling variants, 4D-GS, offers promising prospects for real-time rendering of dynamic surgical scenarios. However, the prerequisite for modeling dynamic scenes…
3D Gaussian Splatting (3DGS) has recently emerged as a powerful representation of geometry and appearance for dense Simultaneous Localization and Mapping (SLAM). Through rapid, differentiable rasterization of 3D Gaussians, many 3DGS SLAM…
Mapping with uncertainty representation is required in many research domains, especially for localization. Although there are many investigations regarding the uncertainty of the pose estimation of an ego-robot with map information, the…
With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring…
We present an approach for efficiently training Gaussian Mixture Model (GMM) by Stochastic Gradient Descent (SGD) with non-stationary, high-dimensional streaming data. Our training scheme does not require data-driven parameter…
The theoretical investigation of gas adsorption, storage, separation, diffusion and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In…
Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a…
This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional…