Related papers: Physics-Embedded Gaussian Process for Traffic Stat…

Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…

Gaussian Processes (GPs) offer an attractive method for regression over small, structured and correlated datasets. However, their deployment is hindered by computational costs and limited guidelines on how to apply GPs beyond simple…

Traditional rule-based physical models are limited by their reliance on singular physical formulas and parameters, making it difficult to effectively tackle the intricate tasks associated with crowd simulation. Recent research has…

The theoretical investigation of gas adsorption, storage, separation, diffusion and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In…

Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

This paper presents DEEGITS (Deep Learning Based Heterogeneous Traffic State Measurement), a comprehensive framework that leverages state-of-the-art convolutional neural network (CNN) techniques to accurately and rapidly detect vehicles and…

Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant…

Accurate prediction of vehicle collision dynamics is crucial for advanced safety systems and post-impact control applications, yet existing methods face inherent trade-offs among computational efficiency, prediction accuracy, and data…

This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the…

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of…

Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic…

Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…

Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…

Accurately modeling and forecasting complex systems governed by partial differential equations (PDEs) is crucial in various scientific and engineering domains. However, traditional numerical methods struggle in real-world scenarios due to…

Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian…

Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…