Related papers: On the Mathematical foundations of Diffusion Monte…
We consider a quantum system coupled to a dissipative background with many degrees of freedom using the Monte Carlo Wave Function method. Instead of dealing with a density matrix which can be very high-dimensional, the method consists of…
We introduce an inferential framework for a wide class of semi-linear stochastic differential equations (SDEs). Recent work has shown that numerical splitting schemes can preserve critical properties of such types of SDEs, give rise to…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
Here, a dichotomy of particles and waves is employed in a quantum Monte Carlo calculation of interacting electrons. Through the creation and propagation of concurrent stochastic ensembles of walkers in physical space and in Hilbert space…
Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
We present an elementary and self-contained account of the analogies existing between classical diffusion and the imaginary-time evolution of quantum systems. These analogies are used to develop a new quantum simulation method which allows…
Diffusion models may be formulated as a time-indexed sequence of energy-based models, where the score corresponds to the negative gradient of an energy function. As opposed to learning the score directly, an energy parameterization is…
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…
Diffusion Monte Carlo (DMC) calculations typically yield highly accurate results in solid-state and quantum-chemical calculations. However, operators that do not commute with the Hamiltonian are at best sampled correctly up to second order…
A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem.…
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…
Monte Carlo methods are state-of-the-art when it comes to dosimetric computations in radiotherapy. However, the execution time of these methods suffers in high-collisional regimes. We address this problem by introducing a kinetic-diffusion…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…
Thermodynamics of dissipative quantum systems with double-well potentials is studied by the path-integral Monte Carlo (PIMC) method without truncation to the two-state model. For efficient simulation at low temperatures, we develop a new…
We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions.…