Related papers: Multi-Level Multi-Fidelity Methods for Path Integr…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
A real-time path integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the…
Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
We propose an improved Path Integral Monte Carlo (PIMC) algorithm called Harmonic PIMC (H-PIMC) and its generalization, Mixed PIMC (M-PIMC). PIMC is a powerful tool for studying quantum condensed phases. However, it often suffers from a low…
Over the last few years, sampling-based stochastic optimal control (SOC) frameworks have shown impressive performances in reinforcement learning (RL) with applications in robotics. However, such approaches require a large amount of samples…
We address the possibility of performing numerical Monte Carlo simulations for the thermodynamics of quantum dissipative systems. Dissipation is considered within the Caldeira-Leggett formulation, which describes the system in the…
In this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and…
Estimating the probability of failure is a critical step in developing safety-critical autonomous systems. Direct estimation methods such as Monte Carlo sampling are often impractical due to the rarity of failures in these systems. Existing…
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…
The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
Model Predictive Path Integral (MPPI) control is a widely used sampling-based approach for real-time control, valued for its flexibility in handling arbitrary dynamics and cost functions. However, it often suffers from high-frequency noise…
We study the numerical integration of functions from isotropic Sobolev spaces $W_p^s([0,1]^d)$ using finitely many function evaluations within randomized algorithms, aiming for the smallest possible probabilistic error guarantee…
The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…
Forecasting the future trajectories of surrounding agents is crucial for autonomous vehicles to ensure safe, efficient, and comfortable route planning. While model ensembling has improved prediction accuracy in various fields, its…
In this article we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of 1-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS…
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…
In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the…
In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a…