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Fermi gases in strongly coupled regimes, such as the unitary limit, are inherently challenging for many-body methods. Although much progress has been made with purely analytic methods, quantitative results require ab initio numerical…
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and…
The multilevel blocking algorithm recently proposed as a possible solution to the sign problem in path-integral Monte Carlo simulations has been extended to systems with long-ranged interactions along the Trotter direction. As an…
Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard to provide high quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation…
In this paper, we consider the implementation of multi-level Monte Carlo method to a stochastic optimal control problem with log-normal coefficients and its surrogate model problem. From the perspective of two optimization problems, i.e.,…
The entanglement entropy probing novel phases and phase transitions numerically via quantum Monte Carlo has made great achievements in large-scale interacting spin/boson systems. In contrast, the numerical exploration in interacting fermion…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
In cohort studies binary outcomes are very often analyzed by logistic regression. However, it is well-known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
Boson sampling is a promising candidate for quantum supremacy. It requires to sample from a complicated distribution, and is trusted to be intractable on classical computers. Among the various classical sampling methods, the Markov chain…
A class of evolution equations with nonlocal diffusion is considered in this work. These are integro-differential equations arising as models of propagation phenomena in continuum media with nonlocal interactions including neural tissue,…
The detection of anisotropies with respect to a given direction in a vector field is a common problem in astronomy. Several methods have been proposed that rely on the distribution of the acute angles between the data and a reference…
Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal…
We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…
The properties of ideal tri-functional dendrimers with forty-five, ninety-three and one hundred and eighty-nine branches are investigated. Three methods are employed to calculate the mean-square radius of gyration, $g$-ratios, asphericity,…
Monte Carlo simulations away from half-filling suffer from a sign problem that can be reduced by deforming the contour of integration. Such a transformation, which induces a Jacobian determinant in the Boltzmann weight, can be implemented…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
Quantum Monte Carlo is one of the most promising approaches for dealing with large-scale quantum many-body systems. It has played an extremely important role in understanding strongly correlated physics. However, two fundamental problems,…
Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…