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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…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
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…
We propose a novel approach to the 'reality gap' problem, i.e., modifying a robot simulation so that its performance becomes more similar to observed real world phenomena. This problem arises whether the simulation is being used by human…
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated…
We extend the application of Hamiltonian Monte Carlo to allow for sampling from probability distributions defined over symmetric or Hermitian positive definite matrices. To do so, we exploit the Riemannian structure induced by Cartan's…
We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign…
Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such random models to obtain statistics on their long-term response.…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
This survey gives an overview of Monte Carlo methodologies using surrogate models, for dealing with densities which are intractable, costly, and/or noisy. This type of problem can be found in numerous real-world scenarios, including…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix…
By means of the Direct Simulation Monte Carlo method, the Boltzmann equation is numerically solved for a gas of hard spheres enclosed between two parallel plates kept at different temperatures and subject to the action of a gravity field…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to…
It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error…
We developed an implicit Particle-in-cell/Monte Carlo model in two-dimensional and axisymmetric geometry for the simulations of the radio-frequency discharges, by introducing several numerical schemes which include variable weights,…
The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…
Given a nonlinear model, a probabilistic forecast may be obtained by Monte Carlo simulations. At a given forecast horizon, Monte Carlo simulations yield sets of discrete forecasts, which can be converted to density forecasts. The resulting…