Related papers: Quantum mechanics and data assimilation
We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space…
Data Assimilation (DA) and Uncertainty quantification (UQ) are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics (CFD) to…
Machine learning algorithms designed to learn dynamical systems from data can be used to forecast, control and interpret the observed dynamics. In this work we exemplify the use of one of such algorithms, namely Koopman operator learning,…
The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…
In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Eulerian penalization of error in the Euclidean space, the Wasserstein metric can capture…
Accurate data assimilation (DA) for systems with piecewise-smooth or discontinuous state variables remains a significant challenge, as conventional covariance-based ensemble Kalman filter approaches often fail to effectively balance…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
Traditional data assimilation uses information obtained from the propagation of one physics-driven model and combines it with information derived from real-world observations in order to obtain a better estimate of the truth of some natural…
Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems…
The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…
Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive…
Data assimilation (DA) integrates numerical model forecasts with observations to achieve the optimal state estimation. Ensemble-based methods, such as the ensemble Kalman filter (EnKF), are widely used for state estimation for…
We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on…
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…
Data assimilation combines forecasts from a numerical model with observations. Most of the current data assimilation algorithms consider the model and observation error terms as additive Gaussian noise, specified by their covariance…
The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…
Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…