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The transport of traffic flow can be modeled by the advection equation. Finite difference and finite volumes methods have been used to numerically solve this hyperbolic equation on a mesh. Advection has also been modeled discretely on…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
An algorithm is developed to optimize vehicle speed trajectory over multiple signalized intersections with known traffic signal information to minimize fuel consumption and travel time, and to meet ride comfort requirements using sequential…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…
We present a new feature extraction method for complex and large datasets, based on the concept of transport operators on graphs. The proposed approach generalizes and extends the many existing data representation methodologies built upon…
Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate…
We present in this paper a very adapted finite volume numerical scheme for transport type-equation. The scheme is an hybrid one combining an anti-dissipative method with down-winding approach for the flux and an high accurate method as the…
This research proposes a novel drift detection methodology for machine learning (ML) models based on the concept of ''deformation'' in the vector space representation of data. Recognizing that new data can act as forces stretching,…
We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…
The auxiliary function method allows computation of extremal long-time averages of functions of dynamical variables in autonomous nonlinear ordinary differential equations via convex optimization. For dynamical systems defined by autonomous…
An important tool for experimental fluids mechanics research is Particle Image Velocimetry (PIV). Several robust methodologies have been proposed to perform the estimation of velocity field from the images, however, alternative methods are…
We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match…
In this paper we describe a high-resolution transport formulation of the regional level-set approach for an improved prediction of the evolution of complex interface networks. The novelty of this method is twofold: (i) construction of local…
We propose to learn a probabilistic motion model from a sequence of images. Besides spatio-temporal registration, our method offers to predict motion from a limited number of frames, useful for temporal super-resolution. The model is based…
We describe the remapped particle-mesh method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In…
Navigating an arbitrary-shaped ground robot safely in cluttered environments remains a challenging problem. The existing trajectory planners that account for the robot's physical geometry severely suffer from the intractable runtime. To…
We present a method, which constructs a suitable deformation vector in loop momentum space, when the loop integration is done numerically with the help of the subtraction method. The method presented here extends previously discussed…
Cartograms are a technique for visually representing geographically distributed statistical data, where values of a numerical attribute are mapped to the size of geographic regions. Contiguous cartograms preserve the adjacencies of the…
Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on…