Related papers: Property-driven State-Space Coarsening for Continu…
Developing a unified small-signal model for modern, large-scale power systems that remains accurate across a wide range of operating ranges presents a formidable challenge. Traditional methods, spanning mechanistic modeling, modal…
Structure-based coarse graining of molecular systems offers a systematic route to reproduce the many-body potential of mean force. Unfortunately, common strategies are inherently limited by the molecular mechanics force field employed.…
We analyze Lindblad-Gorini-Kossakowski-Sudarshan-type generators for selected periodically driven open quantum systems. All these generators can be obtained by temporal coarse-graining procedures, and we compare different coarse-graining…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
Starting from a coarse-grained map of a quantum many-body system, we construct the inverse map that assigns a microscopic state to a coarse-grained state based on the maximum entropy principle. Assuming unitary evolution in the microscopic…
Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is…
In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained…
Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
Coarse-grained molecular dynamics often sacrifices accuracy and transferability for computational efficiency, but the use of machine learned potentials is helping coarse-grained models attain performance on par with atomistic molecular…
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian…
Finite stochastic Markov models play a major role for modelling biochemical pathways. Such models are a coarse-grained description of the underlying microscopic dynamics and can be considered mesoscopic. The level of coarse-graining is to a…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of…
We introduce a straightforward numerical coarse-graining scheme to estimate quantum states for a set of noisy measurement outcomes, which are difficult to calibrate, that is based solely on the measurement data collected from these…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…
As a universal theory of physics, quantum mechanics must assign states to every level of description of a system -- from a full microscopic description, all the way up to an effective macroscopic characterization -- and also to describe the…
ICT systems provide detailed information on computer network traffic. However, due to storage limitations, some of the information on past traffic is often only retained in an aggregated form. In this paper we show that Linear Gaussian…
We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster…
Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The…