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A numerical model and parallel software for 3D simulations of granular flows have been developed based on the Lagrangian particle (LP) method [R.Samulyak, X. Wang, H.-C. Chen, Lagrangian particle method for compressible fluid dynamics, J.…
More powerful feature representations derived from deep neural networks benefit visual tracking algorithms widely. However, the lack of exploitation on temporal information prevents tracking algorithms from adapting to appearances changing…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The…
Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as…
In recent work (arXiv:1006.3100v1), we have presented a novel approach for improving particle filters for multi-target tracking. The suggested approach was based on drift homotopy for stochastic differential equations. Drift homotopy was…
Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that…
We introduce a tracking-by-detection method that integrates a deep object detector with a particle filter tracker under the regularization framework where the tracked object is represented by a sparse dictionary. A novel observation model…
We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…
We present the PSALTer software for efficiently computing the mass and energy of the particle spectrum for any (e.g. higher-rank) tensor field theory in the Wolfram Language. The user must provide a Lagrangian density which is expanded…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
The equations of motion for a Lagrangian ${\cal L}(k_1)$, depending on the curvature $k_1$ of the particle worldline, embedded in a space--time of constant curvature, are considered and reformulated in terms of the principal curvatures. It…
In this paper, we describe a new scalable and modular material point method (MPM) code developed for solving large-scale problems in continuum mechanics. The MPM is a hybrid Eulerian-Lagrangian approach, which uses both moving material…
In this paper, we present a novel method called PolyTrack for fast multi-object tracking and segmentation using bounding polygons. Polytrack detects objects by producing heatmaps of their center keypoint. For each of them, a rough…
We study the filtering problem over a Lie group that plays an important role in robotics and aerospace applications. We present a new particle filtering algorithm based on stochastic control. In particular, our algorithm is based on a…
Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…
Learning data-efficient object dynamics models for robotic manipulation remains challenging, especially for deformable objects. A popular approach is to model objects as sets of 3D particles and learn their motion using graph neural…
Recent advancements in 3D Gaussian Splatting (3DGS) have demonstrated its potential for efficient and photorealistic 3D reconstructions, which is crucial for diverse applications such as robotics and immersive media. However, current…
The key limitations of digital inline holography (DIH) for particle tracking applications are poor longitudinal resolution, particle concentration limits, and case-specific processing. We utilize an inverse problem method with fused lasso…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…