Related papers: A Full-Density Approach to Simulating Random Itera…

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…

This paper proposes a nonparametric multivariate density forecast model based on deep learning. It not only offers the whole marginal distribution of each random variable in forecasting targets, but also reveals the future correlation…

We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…

We present density response estimators for Monte Carlo simulations that are based on a reweighting procedure, where the samples of an unperturbed system are used to estimate the properties of a system perturbed by an external harmonic…

In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…

In this paper a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) using systems of stochastic partial differential equations (SPDEs) has been introduced and applied to simulated data and real data. By solving a…

We present a public code to generate random fields with an arbitrary probability distribution function (PDF) and an arbitrary correlation function. The algorithm is cosmology-independent, applicable to any stationary stochastic process over…

A mapping of the process on a continuous configuration space to the symbolic representation of the motion on a discrete state space will be combined with an iterative aggregation and disaggregation (IAD) procedure to obtain steady state…

Optimization of Reconfigurable Intelligent Surfaces (RIS) via a previously introduced method is effective, but time-consuming, because multiport impedance or scatter matrices are required for each transmitter and receiver position, which…

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…

Dense flow visualization is a popular visualization paradigm. Traditionally, the various models and methods in this area use a continuous formulation, resting upon the solid foundation of functional analysis. In this work, we examine a…

Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple…

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…

The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this paper we develop…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…