Related papers: Dynamic Mode Decomposition for Extrapolating Non-e…

Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been…

Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…

F.E. Harris has been a significant partner in our work on orbital-free density functional approximations for use in ab initio molecular dynamics. Here we mention briefly the essential progress on single-point functionals since our original…

This work describes a novel simulation approach that combines machine learning and device modelling simulations. The device simulations are based on the quantum mechanical non-equilibrium Greens function (NEGF) approach and the machine…

Within Kirkwood theory, we study the translational diffusion coefficient of a single polymer chain in dilute solution, and focus on the small difference between the short--time Kirkwood value $D^{(K)}$ and the asymptotic long--time value…

Mittag-Leffler analysis is an infinite dimensional analysis with respect to non-Gaussian measures of Mittag-Leffler type which generalizes the powerful theory of Gaussian analysis and in particular white noise analysis. In this paper we…

We implement the GW space-time method at finite temperatures, in which the Green's function G and the screened Coulomb interaction W are represented in the real space on a suitable mesh and in imaginary time in terms of Chebyshev…

The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy…

Due to their conceptual appeal and computational convenience, two-level systems (TLS) and their generalisations are often used to investigate nonlinear behavior in quantum optics, and to assess the applicability of theoretical methods. Here…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…

Dynamic Mode Decomposition (DMD) is a technique to approximate generally non-linear dynamical systems using linear techniques, which are better understood and easier to analyze. Koopman theory extends DMD by transforming the original system…

This work combines for the first time ab initio molecular dynamics (AIMD) within the Born-Oppenheimer approximation, with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The…

The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…

We introduce a novel methodology for simulating the excited-state dynamics of extensive molecular aggregates in the framework of the long-range corrected time-dependent density-functional tight-binding fragment molecular orbital method…

Functional brain dynamics is supported by parallel and overlapping functional network modes that are associated with specific neural circuits. Decomposing these network modes from fMRI data and finding their temporal characteristics is…

We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu-Paz-Zhang master equation of quantum…

Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…

Orbital-Free Density Functional Theory (OFDFT) has re-emerged as a viable alternative to Kohn-Sham DFT, driven by recent advances in kinetic energy density functionals (KEDFs). Nonlocal (NL) KEDFs have significantly extended OFDFT's…

This paper introduces the discrete-velocity-direction model (DVDM) in conjunction with the hyperbolic quadrature method of moments (HyQMOM) to develop a multidimensional spatial-temporal approximation of the BGK equation, termed DVD-HyQMOM.…

We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of $O(N_{\rm e}^3$), where $N_{\rm e}$ is the number of electrons. The cubic scaling…