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Many problems can be formulated as high-dimensional integrals of discontinuous functions that exhibit significant boundary growth, challenging the error analysis and applications of randomized quasi-Monte Carlo (RQMC) methods. This paper…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be…

This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus…

In this paper, we propose a general analysis framework for inexact power iteration, which can be used to efficiently solve high dimensional eigenvalue problems arising from quantum many-body problems. Under the proposed framework, we…

The Monte Carlo calculation of R\'enyi entanglement entropies $S^{}_n$ of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few…

This paper investigates methods for estimating the optimal stochastic control policy for a Markov Decision Process with unknown transition dynamics and an unknown reward function. This form of model-free reinforcement learning comprises…

We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…

Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…

We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…

The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…

Wavefunction correction scheme, which was developed as a variance reduction tool for the pure and fixed-node diffusion Monte Carlo (DMC) computations by Anderson and Freihaut, is applied to the DMC computations of fermions without using the…

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…

We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient…

We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…

The direct simulation Monte Carlo (DSMC) method is a widely used stochastic particle approach to solving the Boltzmann equation. However, its computational cost remains a major drawback, which can be attributed to statistical errors when…

We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by a generalized exchange statistics. This method, initially proposed for continuum systems, introduces a…

In this work, we report, for the first time, an implementation of fermionic auxiliary-field quantum Monte Carlo (AFQMC) using matrix product state (MPS) trial wavefunctions, dubbed MPS-AFQMC. Calculating overlaps between an MPS trial and…

Recent studies on diffusion-based sampling methods have shown that Langevin Monte Carlo (LMC) algorithms can be beneficial for non-convex optimization, and rigorous theoretical guarantees have been proven for both asymptotic and finite-time…

We propose an end-to-end integrated strategy to produce highly accurate quantum chemistry (QC) synthetic datasets (energies and forces) aimed at deriving Foundation Machine Learning models for molecular simulation. Starting from Density…