Related papers: Spectral Coarse Graining and Synchronization in Os…
We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations for characteristic scales identified through the spectral gap. This method retains both diffusion…
To investigate the impact of non-linear interactions on dynamic coarse graining, we study a simplified model system, featuring a tracer particle in a complex environment. Using a projection operator formalism and computer simulations, we…
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…
Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the…
We propose and illustrate an approach to coarse-graining the dynamics of evolving networks (networks whose connectivity changes dynamically). The approach is based on the equation-free framework: short bursts of detailed network evolution…
Very recently, a kind of spatial network constructed with power-law distance distribution and total energy constriction is proposed. Moreover, it has been pointed out that such spatial networks have the optimal exponents $\delta$ in the…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization…
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 explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems,…
Contagion dynamics in complex networks drive critical phenomena such as epidemic spread and information diffusion,but their analysis remains computationally prohibitive in large-scale, high-complexity systems. Here, we introduce the…
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…
Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…
Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and, ultimately, design. Here we propose and illustrate a systematic and powerful approach to…
In recent years, simulation methods based on the scaling of atomic potential functions, such as quasi-coarse-grained dynamics and coarse-grained dynamics, have shown promising results for modeling crystalline systems at multiple scales.…
Oscillator networks represent a promising technology for unconventional computing and artificial intelligence. Thus far, these systems have primarily been demonstrated in small-scale implementations, such as Ising Machines for solving…
We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic…
We perform the renormalization-group-like numerical analysis of geographically embedded complex networks on the two-dimensional square lattice. At each step of coarsegraining procedure, the four vertices on each $2 \times 2$ square box are…