相关论文: Failure of LMC statistical complexity in identifyi…
Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity.…
Mixed state entanglement measures can act as a versatile probes of many-body systems. However, they are generally hard to compute, often relying on tricky optimizations. One measure that is straightforward to compute is the logarithmic…
The reliability of a complex industrial system can rarely be assessed analytically. As system failure is often a rare event, crude Monte-Carlo methods are prohibitively expensive from a computational point of view. In order to reduce…
We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number…
In this paper, we investigate when system identification is statistically easy or hard, in the finite sample regime. Statistically easy to learn linear system classes have sample complexity that is polynomial with the system dimension. Most…
We introduce new diagnostics of the transition between the ergodic and many-body localization phases, which are based on complexity measures defined via the probability distribution function of the Lanczos coefficients of the…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…
We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the…
This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
We study the Hamiltonian dynamics of a many-body quantum system subjected to periodic projective measurements which leads to probabilistic cellular automata dynamics. Given a sequence of measured values, we characterize their dynamics by…
Nested Monte Carlo is widely used for risk estimation, but its efficiency is limited by the discontinuity of the indicator function and high computational cost. This paper proposes a nested Multilevel Monte Carlo (MLMC) method combined with…
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic…
The description of complex systems requires a progressively larger number of parameters. However, in practice, it often happens that a small subset of parameters suffices to describe the dynamics of the system itself: these combinations are…