Related papers: A non-equilibrium Monte Carlo approach to potentia…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation…
Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…
The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained…
We investigate an inverse boundary value problem of determination of a nonlinear law for reaction-diffusion processes, which are modeled by general form semilinear parabolic equations. We do not assume that any solutions to these equations…
Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…
Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…
Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…
This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
The wavelength of a periodic spatial structure of Turing type is an intrinsic property of the considered reaction-diffusion dynamics and we address the question of its control at the microscopic scale for given dynamical parameters. The…
We use replica exchange Monte-Carlo simulations to measure the equilibrium equation of state of the disordered fluid state for a binary hard sphere mixture up to very large densities where standard Monte-Carlo simulations do not easily…
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…
Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…
Knowledge of exact analytical functional forms for the pair correlation function $g_2(r)$ and its corresponding structure factor $S(k)$ of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly…
Monte Carlo is famous for accepting model extensions and model refinements up to infinite dimension. However, this powerful incremental design is based on a premise which has severely limited its application so far: a state-variable can…
We extend to quenched disordered systems the variational scheme for real space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
Monte Carlo algorithms are barely considered in spin foam quantum gravity. Due to the quantum nature of spin foam amplitudes one cannot readily apply them, and the present sign problem is a threat to convergence and thus efficiency. Yet,…