Related papers: Accelerating Posterior sampling for Scalable Gauss…

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of…

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…

In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…

This paper focuses on Bayesian Optimization in combinatorial spaces. In many applications in the natural science. Broad applications include the study of molecules, proteins, DNA, device structures and quantum circuit designs, a on…

A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to…

Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…

The conjugate gradient method (CG) is typically used with a preconditioner which improves efficiency and robustness of the method. Many preconditioners include parameters and a proper choice of a preconditioner and its parameters is often…

Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian…

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…

Among generalized additive models, additive Mat\'ern Gaussian Processes (GPs) are one of the most popular for scalable high-dimensional problems. Thanks to their additive structure and stochastic differential equation representation,…

Multiscale modeling is a systematic approach to describe the behavior of complex systems by coupling models from different scales. The approach has been demonstrated to be very effective in areas of science as diverse as materials science,…

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…

Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.…

Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based…