Related papers: Making big steps in trajectories
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…
Smooth dynamics interrupted by discontinuities are known as hybrid systems and arise commonly in nature. Latent ODEs allow for powerful representation of irregularly sampled time series but are not designed to capture trajectories arising…
We investigate a family of approximate multi-step proximal point methods, accelerated by implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…
We tackle the problem of estimating optical flow from a monocular camera in the context of autonomous driving. We build on the observation that the scene is typically composed of a static background, as well as a relatively small number of…
Particle tracking in large-scale numerical simulations of turbulent flows presents one of the major bottlenecks in parallel performance and scaling efficiency. Here, we describe a particle tracking algorithm for large-scale parallel…
In recent years, consumer-level depth cameras have been adopted for various applications. However, they often produce depth maps at only a moderately high frame rate (approximately 30 frames per second), preventing them from being used for…
An improved fully polynomial-time approximation scheme and a greedy heuristic for the fractional length-bounded maximum multicommodity flow problem with unit edge-lengths are proposed. Computational experiments are carried out on benchmark…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
The optical flow of humans is well known to be useful for the analysis of human action. Given this, we devise an optical flow algorithm specifically for human motion and show that it is superior to generic flow methods. Designing a method…
Deep homography estimation has broad applications in computer vision and robotics. Remarkable progresses have been achieved while the existing methods typically treat it as a direct regression or iterative refinement problem and often…
High-fidelity flow simulations are indispensable when analyzing systems exhibiting multiphase flow phenomena. The accuracy of multiphase flow simulations is strongly contingent upon the finest mesh resolution used to represent the…
Handling all together large displacements, motion details and occlusions remains an open issue for reliable computation of optical flow in a video sequence. We propose a two-step aggregation paradigm to address this problem. The idea is to…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
This paper addresses the problem of finding multiple near-optimal, spatially-dissimilar paths that can be considered as alternatives in the decision making process, for finding optimal corridors in which to construct a new road. We further…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
The homotopy continuation method has been widely used in solving parametric systems of nonlinear equations. But it can be very expensive and inefficient due to singularities during the tracking even though both start and end points are…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…