Related papers: Gaussian dynamics equation in normal product form
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…
Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…
The density matrix renormalization group (DMRG) is applied to some one-dimensional reaction-diffusion models in the vicinity of and at their critical point. The stochastic time evolution for these models is given in terms of a non-symmetric…
This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…
The temporal evolution of quantum statistical properties of an interacting atom-radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes-Cummings model. To…
In this short note we address a gaussian property of normal vectors in random non-Hermitian matrices. The approach uses a simple geometric and comparison technique.
Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature, efficient numerical methods for models based on it are uncommon…
The explicit dynamics of the moments for the GKSL equation and the approach in finding stationary Gaussian states are obtained. In our case the GKSL equation corresponds to Wiener stochastic processes. Such equations contain a double…
We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while…
We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nos\'e-Hoover, our algorithm is based on a non-Hamiltonian…
Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme, if not accurate…
In this paper we propose a generalized Gaussian process concurrent regression model for functional data where the functional response variable has a binomial, Poisson or other non-Gaussian distribution from an exponential family while the…
By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The…
Gromov-Wasserstein (GW) transport is inherently invariant under isometric transformations of the data. Having this property in mind, we propose to estimate dynamical systems by transfer operators derived from GW transport plans, when merely…
Within a Lagrangian formalism we derive the time-dependent Gutzwiller approximation for general multi-band Hubbard models. Our approach explicitly incorporates the coupling between time-dependent variational parameters and a time-dependent…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…
We present a novel kernel over the space of probability measures based on the dual formulation of optimal regularized transport. We propose an Hilbertian embedding of the space of probabilities using their Sinkhorn potentials, which are…
We reformulate time evolution of systems in mixed states in terms of the classical observables of correlators using the Weyl correspondence rule. The resulting equation of motion for the Wigner functional of the density matrix is found to…
Understanding the intricate properties of one-dimensional quantum systems coupled to multiple reservoirs poses a challenge to both analytical approaches and simulation techniques. Fortunately, density matrix renormalization group-based…