Related papers: Approximating the long time average of the density…
Ensemble models refer to methods that combine a typically large number of classifiers into a compound prediction. The output of an ensemble method is the result of fitting a base-learning algorithm to a given data set, and obtaining diverse…
We analyze the recently developed folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] to simulate the dynamics of infinite quantum spin chains, and relate its performance to the kind of entanglement produced under the evolution of…
This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…
Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from…
Motivated by applications to 3D printing, this paper presents two algorithms for calculating an ensemble of solutions to heat conduction problems. The ensemble average is the most likely temperature distribution and its variance gives an…
We study quantum quenches in the XXZ spin-$1/2$ Heisenberg chain from families of ferromagnetic and antiferromagnetic initial states. Using Bethe ansatz techniques, we compute short-range correlators in the complete generalized Gibbs…
Ensembles improve prediction performance and allow uncertainty quantification by aggregating predictions from multiple models. In deep ensembling, the individual models are usually black box neural networks, or recently, partially…
The class imbalance problem is important and challenging. Ensemble approaches are widely used to tackle this problem because of their effectiveness. However, existing ensemble methods are always applied into original samples, while not…
We study the time evolution of correlation functions in closed quantum systems for nonequilibrium ensembles of initial conditions. For a scalar quantum field theory we show that generic time-reversal invariant evolutions approach…
Differences between time-averaged and ensemble-averaged wind are studied for the case of changing wind direction. We consider a flow driven by a temporally turning pressure gradient in both an idealized case of a staggered cube array and a…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
To bypass the reliance on local observables in verifying the eigenstate thermalization hypothesis (ETH), we introduce an observable-independent measure of distinguishability based on the variance of a rescaled local operator. We establish a…
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
We simulate the collective dynamics in spin lattices with long range interactions and collective decay in one, two and three dimensions. Starting from a dynamical mean-field approach derived by local factorization of the density operator we…
We propose a new approach to justify the use of the microcanonical ensemble for isolated macroscopic quantum systems. Since there are huge number of independent observables in a macroscopic system, we cannot see all of them. Actually what…
Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…
Recent results, extending the Schmidt decomposition theorem to wavefunctions of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is…
This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear…