Related papers: Macroscopic Traffic Flow Modeling with Physics Reg…

We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction,…

The ability of Gaussian processes (GPs) to predict the behavior of dynamical systems as a more sample-efficient alternative to parametric models seems promising for real-world robotics research. However, the computational complexity of GPs…

Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…

Gaussian Process Regression (GPR) is a powerful tool for nonparametric regression, but its application in a fully Bayesian fashion in high-dimensional settings is hindered by two primary challenges: the difficulty of variable selection and…

Collecting operationally realistic data to inform machine learning models can be costly. Before collecting new data, it is helpful to understand where a model is deficient. For example, object detectors trained on images of rare objects may…

For autonomous mobile robots, uncertainties in the environment and system model can lead to failure in the motion planning pipeline, resulting in potential collisions. In order to achieve a high level of robust autonomy, these robots should…

A computational method based on the non-linear Gaussian process (GP), known as deep Gaussian processes (deep GPs) for uncertainty quantification & propagation in modelling of flow through heterogeneous porous media is presented. The method…

One of the key challenges in revenue management is unconstraining demand data. Existing state of the art single-class unconstraining methods make restrictive assumptions about the form of the underlying demand and can perform poorly when…

Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

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…

Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models,…

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often…

Long-span bridges are subjected to a multitude of dynamic excitations during their lifespan. To account for their effects on the structural system, several load models are used during design to simulate the conditions the structure is…

We present an approach for satisfying state constraints in systems with nonparametric uncertainty by estimating this uncertainty with a real-time-update Gaussian process (GP) model. Notably, new data is incorporated into the model in real…

Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…

Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model…

Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…

Driving under varying road conditions is challenging, especially for autonomous vehicles that must adapt in real-time to changes in the environment, e.g., rain, snow, etc. It is difficult to apply offline learning-based methods in these…