Related papers: A polynomial-based Monte Carlo approach for estima…
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,…
Real-time safety systems are crucial components of intelligent vehicles. This paper introduces a prediction-based collision risk assessment approach on highways. Given a point mass vehicle dynamics system, a stochastic forward reachable set…
The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and…
We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at…
Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…
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…
In statistical data assimilation (SDA) and supervised machine learning (ML), we wish to transfer information from observations to a model of the processes underlying those observations. For SDA, the model consists of a set of differential…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
In this paper, novel approaches are developed to explore the dynamics of motion in periodic orbits near libration points in cislunar space using the Differential Algebra (DA) framework. The Circular Restricted Three-Body Problem (CR3BP)…
Uncertainty estimation is a key issue when considering the application of deep neural network methods in science and engineering. In this work, we introduce a novel algorithm that quantifies epistemic uncertainty via Monte Carlo sampling…
The montecarlo method, which is quite commonly used to solve maximum entropy problems in statistical physics, can actually be used to solve inverse problems in a much wider context. The probability distribution which maximizes entropy can…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
In this work we develop an effective Monte Carlo method for estimating sensitivities, or gradients of expectations of sufficiently smooth functionals, of a reflected diffusion in a convex polyhedral domain with respect to its defining…
A new approach to simulation of stationary flows by Direct Simulation Monte Carlo method is proposed. The idea is to specify an individual time step for each component of a gas mixture. The approach consists of modifications mainly to…
A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density…
An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) estimator for approximating the integral of a multivariate…