Related papers: Physics-Informed Gaussian Process Inference of Liq…
We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem…
Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Recent advances in 3D Gaussian Splatting have enabled impressive photorealistic novel view synthesis. However, to transition from a pure rendering engine to a reliable spatial map for autonomous agents and safety-critical applications,…
Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…
We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…
Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data…
We present a Gaussian Process (GP) approach (Gaussian Process Hydrodynamics, GPH) for approximating the solution of the Euler and Navier-Stokes equations. As in Smoothed Particle Hydrodynamics (SPH), GPH is a Lagrangian particle-based…
Motivated by the analysis of spectrometric data, we introduce a Gaussian graphical model for learning the dependence structure among frequency bands of the infrared absorbance spectrum. The spectra are modeled as continuous functional data…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
Bayesian neural networks attempt to combine the strong predictive performance of neural networks with formal quantification of uncertainty associated with the predictive output in the Bayesian framework. However, it remains unclear how to…
The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem: given parameter inputs, solve the governing equations to determine output quantities of interest. In…
Seismic fragility curves have been introduced as key components of Seismic Probabilistic Risk Assessment studies. They express the probability of failure of mechanical structures conditional to a seismic intensity measure and must take into…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…
A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged…