Related papers: Quantum mechanics and data assimilation
Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
This paper introduces a data assimilation (DA) framework based on the extended Kalman filter-cell transmission model, designed to assist jam-absorption driving (JAD) operation to alleviate sag traffic congestion. To ascertain and…
Global information about dynamical systems can be extracted by analysing associated infinite-dimensional transfer operators, such as Perron-Frobenius and Koopman operators as well as their infinitesimal generators. In practice, these…
The study of quantum mechanics in non-inertial reference frames, particularly in the context of open systems, introduces several intriguing phenomena and challenges. This paper presents a comprehensive framework for analyzing the quantum…
Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…
The resources required to characterise the dynamics of engineered quantum systems-such as quantum computers and quantum sensors-grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…
In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are…
Abrupt transitions ("tipping") in nonlinear dynamical systems are often accompanied by changes in the geometry of the attracting set, but quantifying such changes from partial and noisy observations in high-dimensional systems remains…
Koopman operator theory and Willems' fundamental lemma both can provide (approximated) data-driven linear representation for nonlinear systems. However, choosing lifting functions for the Koopman operator is challenging, and the quality of…
Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the…
Data imputation is a critical step in data pre-processing, particularly for datasets with missing or unreliable values. This study introduces a novel quantum-inspired imputation framework evaluated on the UCI Diabetes dataset, which…
The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…
This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and…
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…
We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the…
Image-based, patient-specific modelling of hemodynamics can improve diagnostic capabilities and provide complementary insights to better understand the hemodynamic treatment outcomes. However, computational fluid dynamics simulations remain…
A correspondence is established between measure-preserving, ergodic dynamics of a classical harmonic oscillator and a quantum mechanical gauge theory on two-dimensional Minkowski space. This correspondence is realized through an isometric…