Related papers: A Dynamics-Informed Gaussian Process Framework for…
We consider a stochastic model which describes the motion of a 2D incompressible fluid in a unbounded domain with viscosity and memory effects. This model is different from the classical stochastic Navier-Stokes-Voigt equations due to the…
Leveraging autonomous systems in safety-critical scenarios requires verifying their behaviors in the presence of uncertainties and black-box components that influence the system dynamics. In this work, we develop a framework for verifying…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…
Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…
A coarse-grained particle model for incompressible Navier-Stokes (NS) equation is proposed based on spatial filtering by utilizing smoothed particle hydrodynamics (SPH) approximations. This model is similar to our previous developed SPH…
In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier-Stokes equations on staggered space-time adaptive Cartesian grids (AMR) in two and three…
Gaussian process (GP) emulators have become essential tools for approximating complex simulators, significantly reducing computational demands in optimization, sensitivity analysis, and model calibration. While traditional GP emulators…
Quasi-periodicity refers to a pattern in a function where it appears periodic but has evolving amplitudes over time. This is often the case in practical settings such as the modeling of case counts of infectious disease or the carbon…
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian…
In this work, we study the class of stochastic process that generalizes the Ornstein-Uhlenbeck processes, hereafter called by \emph{Generalized Ornstein-Uhlenbeck Type Process} and denoted by GOU type process. We consider them driven by the…
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…
This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression…
We study the transport of Gaussian measures under the flow of the 2-dimensional defocusing Schr\"odinger equation $i \partial_t u + \Delta u = |u|^{2k} u$ posed on $\mathbb T^2$. In particular, we show that the Gaussian measures with…
Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to…
Recent advancements in data-driven aeroelasticity have been driven by the wealth of data available in the wind engineering practice, especially in modeling aerodynamic forces. Despite progress, challenges persist in addressing free-stream…
This paper presents a joint theoretical and numerical study of a stochastic version of the compressible Navier-Stokes equations within the location uncertainty (LU) framework, applied to problems related to upper ocean vertical mixing. This…