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A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
This paper considers enforcing safety and stability of dynamical systems in the presence of model uncertainty. Safety and stability constraints may be specified using a control barrier function (CBF) and a control Lyapunov function (CLF),…
Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several…
The development of efficient numerical methods for kinetic equations with stochastic parameters is a challenge due to the high dimensionality of the problem. Recently we introduced a multiscale control variate strategy which is capable to…
Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
Computational fluid dynamics (CFD) can be used to simulate vascular haemodynamics and analyse potential treatment options. CFD has shown to be beneficial in improving patient outcomes. However, the implementation of CFD for routine clinical…
A new approach to the steady state detection in the uniformization method of solving continuous time Markov chains is introduced. The method is particularly useful in solving inhomogenous CTMC's in multiple steps, where the desired error…
While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for \textit{ab initio} electronic structure calculations, in practice the fermionic sign problem necessitates the use of the fixed-node approximation and trial…
Discrete diffusion models have emerged as powerful frameworks for generating structured categorical data. However, efficiently sampling from reward-tilted distributions remains a fundamental challenge. While Twisted Sequential Monte Carlo…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based…
This paper presents the first implementation of a coupling between advanced wave function theories and molecular density functional theory (MDFT). This method enables the modeling of solvent effect into quantum mechanical (QM) calculations…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
The aim of this article is to present a comprehensive methodology for the verification of computational fluid dynamics (CFD) solvers with a special attention to aspects pertinent to discretizations with orders of accuracy (OOAs) higher than…
The multilevel Monte Carlo (MLMC) method is highly efficient for estimating expectations of a functional of a solution to a stochastic differential equation (SDE). However, MLMC estimators may be unstable and have a poor (noncanonical)…
We report on the development of a test-particle based kinetic Monte Carlo code for large systems and its application to simulate matter in the continuum regime. Our code combines advantages of the Direct Simulation Monte Carlo and the…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range…