Related papers: Adaptive RKHS Fourier Features for Compositional G…

We define Recurrent Gaussian Processes (RGP) models, a general family of Bayesian nonparametric models with recurrent GP priors which are able to learn dynamical patterns from sequential data. Similar to Recurrent Neural Networks (RNNs),…

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and…

Multi-output Gaussian processes (MOGPs) have been introduced to deal with multiple tasks by exploiting the correlations between different outputs. Generally, MOGPs models assume a flat correlation structure between the outputs. However,…

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…

Electron ptychography enables dose-efficient atomic-resolution imaging, but conventional reconstruction algorithms suffer from noise sensitivity, slow convergence, and extensive manual hyperparameter tuning for regularization, especially in…

We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes…

Finite element model updating utilizing frequency response functions as inputs is an important procedure in structural analysis, design and control. This paper presents a highly efficient framework that is built upon Gaussian process…

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…

Deep kernel learning (DKL) leverages the connection between Gaussian process (GP) and neural networks (NN) to build an end-to-end, hybrid model. It combines the capability of NN to learn rich representations under massive data and the…

The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local…

We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation…

The Hilbert-space Gaussian Process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian Process (GP) inference by projecting the GP onto M basis functions. These properties result in a…

Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes…

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…

The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…