Related papers: Monte Carlo Basin Bifurcation Analysis
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
Recently, there has been significant advancement in the machine learning (ML) approach and its application to diverse systems ranging from complex to quantum systems. As one of such systems, a coupled-oscillators system exhibits intriguing…
We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…
We propose a dual-channel reservoir-computing scheme for inferring the dynamics of two distinct chaotic systems with a single machine. By augmenting a standard reservoir with a system-label channel and a parameter-control channel, the…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
The examination of uncertainty in the predictions of machine learning (ML) models is receiving increasing attention. One uncertainty modeling technique used for this purpose is Monte-Carlo (MC)-Dropout, where repeated predictions are…
Bi-clustering is a useful approach in analyzing biological data when observations come from heterogeneous groups and have a large number of features. We outline a general Bayesian approach in tackling bi-clustering problems in moderate to…
The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of…
In this work, we discuss the implications of a recently obtained equilibrium fluctuation-dissipation relation on the extension of the available Monte Carlo methods based on the consideration of the Gibbs canonical ensemble to account for…
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…
In a Nature article, Scheffer et al. presented a novel data-driven framework to predict critical transitions in complex systems. These transitions, which may stem from failures, degradation, or adversarial actions, have been attributed to…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation…
We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…
Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate…
DBSCAN and OPTICS are powerful algorithms for identifying clusters of points in domains where few assumptions can be made about the structure of the data. In this paper, we leverage these strengths and introduce a new algorithm, LINSCAN,…
Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…
A new unbiased Monte Carlo technique called Tensor Network Monte Carlo (TNMC) is introduced based on sampling all possible renormalizations (or course-grainings) of tensor networks, in this case matrix-product states. Tensor networks are a…
Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…