Related papers: A data-driven and model-based accelerated Hamilton…

We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective. Our main goal is to make standard, `out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models by…

Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…

This paper introduces a novel hierarchical Bayesian model specifically designed to address challenges in Inverse Uncertainty Quantification (IUQ) for time-dependent problems in nuclear Thermal Hydraulics (TH) systems. The unique…

We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target…

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate…

Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a powerful method of Bayesian inference that exploits underlying geometric information of the posterior distribution in order to efficiently traverse the parameter space. However, the…

Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…

In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…

Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) method for performing approximate inference in complex probabilistic models of continuous variables. In common with many MCMC methods, however, the standard HMC…

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…

Bayesian formulation of modern day signal processing problems has called for improved Markov chain Monte Carlo (MCMC) sampling algorithms for inference. The need for efficient sampling techniques has become indispensable for high…

The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…

Markov Chain Monte Carlo inference of target posterior distributions in machine learning is predominately conducted via Hamiltonian Monte Carlo and its variants. This is due to Hamiltonian Monte Carlo based samplers ability to suppress…

Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog"…

We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE. The main idea is to repeatedly solve its linearization by using the quasi-reversibility…