Related papers: Physics-Informed Gaussian Process Inference of Liq…

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

A gaussian distribution of binding energies, but conditioned to exploit generally available information on packing in liquids, provides a statistical-thermodynamic theory of liquid water that is structurally non-committal, molecularly…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…

A mathematical model is developed, to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random…

This dissertation is founded on the central notion that structural correlations in dense fluids, such as dense gases, liquids, and glasses, are directly related to fundamental interatomic forces. This relationship was identified early in…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…

Constitutive model discovery refers to the task of identifying an appropriate model structure, usually from a predefined model library, while simultaneously inferring its material parameters. The data used for model discovery are measured…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to…

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…

Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions,…

Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

We study Spatial Logistic Gaussian Process (SLGP) models for non-parametric estimation of probability density fields using scattered samples of heterogeneous sizes. SLGPs are examined from the perspective of random measures and their…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…