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Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…
In particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…
We argue that one can associate a pseudo-time with sequences of configurations generated in the course of classical Monte Carlo simulations for a single-minimum bound state, if the sampling is optimal. Hereby the sampling rates can be,…
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about…
A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB) polymer mixture. By applying the equal peak-weight criterion to the…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi- infinite…
Causal inference requires evaluating models on balanced distributions between treatment and control groups, while training data often exhibits imbalance due to historical decision-making policies. Most conventional statistical methods…
Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…
We discuss different approaches for studying the influence of disorder in the three-dimensional Ising model. From the theoretical point of view, renormalisation group calculations provide quite accurate results. Experiments carried out on…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
Inverse methods of statistical mechanics are becoming productive tools in the design of materials with specific microstructures or properties. While initial studies have focused on solid-state design targets (e.g, assembly of colloidal…
The work is devoted to the study of the inverse problem of determining the right-hand side of a nonlinear subdiffusion equation with a Caputo derivative with respect to time. Nonlinearity of the equation means that the right-hand side of…
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…
We investigate the quality of structural models generated by the Reverse Monte Carlo (RMC) method in a typical application to amorphous systems. To this end we calculate surrogate diffraction data from a Li2O-SiO2 molecular dynamics (MD)…
We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD)…