Related papers: Gradient Navigation Model for Pedestrian Dynamics

As power systems transition toward renewable-rich and inverter-dominated operations, accurate time-domain dynamic analysis becomes increasingly critical. Such analysis supports key operational tasks, including transient stability…

Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…

Data-driven modeling of constrained multibody dynamics remains challenged by (i) the training cost of Neural ODEs, which typically require backpropagation through an ODE solver, and (ii) error accumulation in rollout predictions. We…

Following the seminal work of Nesterov, accelerated optimization methods have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios where second-order optimization strategies are…

Encoding frequency stability constraints in the operation problem is challenging due to its complex dynamics. Recently, data-driven approaches have been proposed to learn the stability criteria offline with the trained model embedded as a…

We present a mathematical model to predict pedestrian motion over a finite horizon, intended for use in collision avoidance algorithms for autonomous driving. The model is based on a road map structure, and assumes a rational pedestrian…

Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…

Pedestrian trajectory prediction is an active research area with recent works undertaken to embed accurate models of pedestrians social interactions and their contextual compliance into dynamic spatial graphs. However, existing works rely…

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…

This work presents a density-based framework for safe navigation in dynamic environments characterized by time-varying obstacle sets and time-varying target regions. We propose an analytical construction of time-varying density functions…

Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…

In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space…

Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these…

Pedestrian trajectory prediction is the key technology in many applications for providing insights into human behavior and anticipating human future motions. Most existing empirical models are explicitly formulated by observed human…

Safe autonomous navigation in unknown environments is an important problem for mobile robots. This paper proposes techniques to learn the dynamics model of a mobile robot from trajectory data and synthesize a tracking controller with safety…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

The task of indoor positioning is fundamental to several applications, including navigation, healthcare, location-based services, and security. An emerging field is inertial navigation for pedestrians, which relies only on inertial sensors…

This paper introduces a novel benchmark to study the impact and relationship of built environment elements on pedestrian collision prediction, intending to enhance environmental awareness in autonomous driving systems to prevent pedestrian…

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…