Related papers: Gradient Navigation Model for Pedestrian Dynamics
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…
Representation learning of static and more recently dynamically evolving graphs has gained noticeable attention. Existing approaches for modelling graph dynamics focus extensively on the evolution of individual nodes independently of the…
In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation…
Accurate traffic participant prediction is the prerequisite for collision avoidance of autonomous vehicles. In this work, we predict pedestrians by emulating their own motion planning. From online observations, we infer a mixture density…
One of the most relevant tasks in an intelligent vehicle navigation system is the detection of obstacles. It is important that a visual perception system for navigation purposes identifies obstacles, and it is also important that this…
We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable,…
Predicting human trajectories is a challenging task due to the complexity of pedestrian behavior, which is influenced by external factors such as the scene's topology and interactions with other pedestrians. A special challenge arises from…
This paper is concerned with the theory, construction and application of variable-stepsize implicit Peer two-step methods that are super-convergent for variable stepsizes, i.e., preserve their classical order achieved for uniform stepsizes…
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…
This paper presents a novel context-based approach for pedestrian motion prediction in crowded, urban intersections, with the additional flexibility of prediction in similar, but new, environments. Previously, Chen et. al. combined…
We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…
This paper introduces a space-continuous force-based model for simulating pedestrian dynamics. The main interest of this work is the quantitative description of pedestrian movement through a bottleneck. Measurements of flow and density will…
Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…
This paper presents a novel incremental learning algorithm for pedestrian motion prediction, with the ability to improve the learned model over time when data is incrementally available. In this setup, trajectories are modeled as simple…
We develop new sub-optimality bounds for gradient descent (GD) that depend on the conditioning of the objective along the path of optimization rather than on global, worst-case constants. Key to our proofs is directional smoothness, a…
The gentlest ascent dynamics (GAD) (Nonlinearity, vol. 24, no. 6, p1831, 2011) is a continuous time dynamics coupling both the position and the direction variables to efficiently locate the saddle point with a given index. These saddle…
Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODEs on a collection of spheres. To demonstrate the versatility…
This paper extends the forced-oscillation-based reduced-order model of walking to a model with ankles and feet. A human-inspired paradigm was designed for the ankle dynamics, which results in improved gait characteristics compared to the…
Gradient descent and its variants are widely used in machine learning. However, oracle access of gradient may not be available in many applications, limiting the direct use of gradient descent. This paper proposes a method of estimating…
We developed a machine vision system to automatically capture the dynamics of pedestrians under four different traffic scenarios. By considering the overhead view of each pedestrian as a digital object, the system processes the image…