Related papers: Quantitative coarse-graining of Markov chains
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…
Developing accurate and efficient coarse-grained representations of proteins is crucial for understanding their folding, function, and interactions over extended timescales. Our methodology involves simulating proteins with molecular…
We propose a novel and systematic method for coarse-graining oscillator networks described by phase equations. Our coarse-graining method enables us to obtain the closed coarse-grained equations for a few effective eigenmodes, which is…
Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such…
Coarse-grained (CG) models provide an effective route to reducing the complexity of molecular simulations (MD), but conventional approaches depend heavily on long all-atom MD trajectories to adequately sample configurational space. This…
Constructing atom-resolved states from low-resolution data is of practical importance in many areas of science and engineering. This problem is addressed in this paper in the context of multiscale factorization methods for molecular…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
The dynamics of systems subjected to noise is called Markovian in the absence of memory effects, i.e. when its immediate future only depends on its present. Time correlations in the noise source may generate non-Markovian effects that,…
The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variable $\xi(x)$, where $x$ describes the configuration of the…
We consider the controllability of large-scale linear networked dynamical systems when complete knowledge of network structure is unavailable and knowledge is limited to coarse summaries. We provide conditions under which average…
Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…
Coarse-Graining (CG) models are low resolution approximation of high resolution models, such as all-atomic (AA) models. An effective CG model is expected to reproduce equilibrium values of sufficient physical quantities of its AA model,…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to…
The issue of the parameterization of small-scale dynamics is addressed in the context of passive-scalar turbulence. The basic idea of our strategy is to identify dynamical equations for the coarse-grained scalar dynamics starting from…
We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or non-equilibrium steady states on all time scales. We unravel a deep connection…
This work presents a systematic methodology for describing the transient dynamics of coarse-grained molecular systems inferred from all-atom simulated data. We suggest Langevin-type dynamics where the coarse-grained interaction potential…
Developing physics-based models for molecular simulation requires fitting many unknown parameters to diverse experimental datasets. Traditionally, this process is piecemeal and difficult to reproduce, leading to a fragmented landscape of…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
Inspired by holographic Wilsonian renormalization, we consider coarse graining a quantum system divided between short distance and long distance degrees of freedom, coupled via the Hamiltonian. Observations using purely long distance…