Related papers: Electrostatics-based particle sampling and approxi…
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
We introduce $\Psi$-Sampler, an SMC-based framework incorporating pCNL-based initial particle sampling for effective inference-time reward alignment with a score-based generative model. Inference-time reward alignment with score-based…
We study collections of point masses which move freely along the real line and stick together when they collide via perfectly inelastic collisions. We quantify the way particles stick together and explain how to associate a probability…
We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or…
In this paper, we introduce a new algorithm for rare event estimation based on adaptive importance sampling. We consider a smoothed version of the optimal importance sampling density, which is approximated by an ensemble of interacting…
We use computer simulations to study highly dense systems of granular particles that are driven by oscillating forces. We implement different dissipation mechanisms that are used to extract the injected energy. In particular, the action of…
In this article, we study the dynamics of a nonlinear system governed by an ordinary differential equation under the combined influence of fast periodic sampling with period $\delta$ and small jump noise of size $\varepsilon, 0<…
The Integrated Nested Laplace Approximation (INLA) is a deterministic approach to Bayesian inference on latent Gaussian models (LGMs) and focuses on fast and accurate approximation of posterior marginals for the parameters in the models.…
For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. This paper presents, within the context of uncertainty…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…
This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…
The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean \cite{mckean1966class}. The interacting diffusions pave a way to…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
We investigate the electrostatic interactions between two charged anisotropic conductors using a combination of asymptotic and numerical methods. For widely separated particles, we employ the method of reflections to analyze the…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm…
We present a brief review on the Impulse Approximation method to study processes of scattering off composite particles. We first construct the model in a non-relativistic fashion that enables us to extend the model to a covariant Impulse…