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We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
For some models of interacting fermions the known solution to the notorious sign-problem in Monte Carlo (MC) simulations is to work with macroscopic fermionic determinants; the price, however, is a macroscopic scaling of the numerical…
We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo…
A Monte Carlo model was used to study the scattering error of an absorption meter with a divergent light beam and a limited acceptance angle of the receiver. Reflections at both ends of the tube were taken into account. Calculations of the…
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
We develop a diagrammatic Monte Carlo method for the real-time dynamics of dissipative quantum impurity models. These are small open quantum systems with interaction and local Markovian dissipation, coupled to a large quantum bath. Our…
Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide…
The primary focus of Monte Carlo simulation is to identify and quantify risk related to uncertainty and variability in spreadsheet model inputs. The stress of Monte Carlo simulation often reveals logical errors in the underlying spreadsheet…
In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…
This work presents stochastic optimization methods targeted at least-squares problems involving Monte Carlo integration. While the most common approach to solving these problems is to apply stochastic gradient descent (SGD) or similar…
We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called…
We propose a method for eliminating the truncation error associated with any subspace diagonalization calculation. The new method, called stochastic error correction, uses Monte Carlo sampling to compute the contribution of the remaining…
A new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is proposed. The method is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which…
This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix…
We explore two complementary modifications of the hybridization-expansion continuous-time Monte Carlo method, aiming at large multi-orbital quantum impurity problems. One idea is to compute the imaginary-time propagation using a matrix…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
We present a whole series of novel methods to alleviate the sign problem of the Fermionic Shadow Wave Function in the context of Variational Monte Carlo. The effectiveness of our new techniques is demonstrated on the example of liquid 3He.…