Related papers: Coarse graining of stochastic differential equatio…

In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice stochastic dynamics. We provide both analytical and numerical evidence that the hierarchy of…

Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large…

We investigate how various coarse-graining methods affect the scaling properties of long-range power-law correlated and anti-correlated signals, quantified by the detrended fluctuation analysis. Specifically, for coarse-graining in the…

Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…

Considering molecular dynamic simulations as a stochastic method, we investigate the possibility of time coarse graining the simulations. Similarly to Boltzmann inversion method in spatial coarse graining, which begins with a free energy…

Lossy data transformations by definition lose information. Yet, in modern machine learning, methods like data pruning and lossy data augmentation can help improve generalization performance. We study this paradox using a solvable model of…

Stochastic modelling of complex systems plays an essential, yet often computationally intensive role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to…

Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…

In established theories of grain coarsening, grains disappear either by shrinking or by rotating as a rigid object to coalesce with an adjacent grain. Here we report a third mechanism for grain coarsening, in which a grain splits apart into…

In this study, a coarse-graining framework for discrete models is formulated on the basis of multiscale homogenization. The discrete model considered in this paper is the Lattice Discrete Particle Model (LDPM), which simulates concrete at…

We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering or electron-electron scattering. These…

In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational…

Many real-world networks display a natural bipartite structure, while analyzing or visualizing large bipartite networks is one of the most challenges. As a result, it is necessary to reduce the complexity of large bipartite systems and…

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…

Many practical techniques for probabilistic inference require a sequence of distributions that interpolate between a tractable distribution and an intractable distribution of interest. Usually, the sequences used are simple, e.g., based on…

High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…

We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial differential equations (PDEs) with large near-kernels, such as…

We show how the mathematical structure of large-deviation principles matches well with the concept of coarse-graining. For those systems with a large-deviation principle, this may lead to a general approach to coarse-graining through the…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity…