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Parking is a critical pillar of driving safety. While recent end-to-end (E2E) approaches have achieved promising in-domain results, robustness under domain shifts (e.g., weather and lighting changes) remains a key challenge. Rather than…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
The progressive hedging algorithm (PHA) is a cornerstone among algorithms for large-scale stochastic programming problems. However, its traditional implementation is hindered by some limitations, including the requirement to solve all…
Topological phase transitions, which do not adhere to Landau's phenomenological model (i.e. a spontaneous symmetry breaking process and vanishing local order parameters) have been actively researched in condensed matter physics. Machine…
This paper presents an efficient method for updating particles in a particle filter (PF) to address the position estimation problem when dealing with sharp-peaked likelihood functions derived from multiple observations. Sharp-peaked…
We investigate the bulldozing motion of a granular sandpile driven forwards by a vertical plate. The problem is set up in the laboratory by emplacing the pile on a table rotating underneath a stationary plate; the continual circulation of…
This paper aims to develop and provide a rigorous treatment to the problem of entropy regularized fine-tuning in the context of continuous-time diffusion models, which was recently proposed by Uehara et al. (arXiv:2402.15194, 2024). The…
Spatially misaligned data can be fused by using a Bayesian melding model that assumes that underlying all observations there is a spatially continuous Gaussian random field process. This model can be used, for example, to predict air…
Estimating the distribution over failures is a key step in validating autonomous systems. Existing approaches focus on finding failures for a small range of initial conditions or make restrictive assumptions about the properties of the…
A numerical model is developed for the simulation of debris flow in landslides over a complex three dimensional topography. The model is based on a lattice, in which debris can be transferred among nearest neighbors according to established…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They…
We introduce a simple and efficient algorithm for diffusion in smoothed particle hydrodynamics (SPH) simulations and apply it to the problem of chemical mixing. Based on the concept of turbulent diffusion, we link the diffusivity of a…
Diffusion models have emerged as the leading paradigm in generative modeling, excelling in various applications. Despite their success, these models often misalign with human intentions and generate results with undesired properties or even…
The work introduces a 3D cellular automaton model for the spatial and crystallographic prediction of spherulite growth phenomena in polymers at the mesoscopic scale. The automaton is discrete in time, real space, and orientation space. The…
This paper is focused on the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The algorithm employs sparse grid collocation in the parameter domain…
Safe and successful deployment of robots requires not only the ability to generate complex plans but also the capacity to frequently replan and correct execution errors. This paper addresses the challenge of long-horizon trajectory planning…
In this paper we use the cellular automaton (CA) approach to model one-dimensional binary diffusion in solids. Employing a very simple state change rule we define an asynchronous CA model and take its continuum limit to obtain the governing…
In studying the predictability of emergent phenomena in complex systems, Israeli & Goldenfeld (Phys. Rev. Lett., 2004; Phys. Rev. E, 2006) showed how to coarse-grain (elementary) cellular automata (CA). Their algorithm for finding…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…