Related papers: Weak Galilean invariance as a selection principle …
A coarse-grained simulation model eliminates microscopic degrees of freedom and represents a polymer by a simplified structure. A priori, two classes of coarse-grained models may be distinguished: those which are designed for a specific…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
The problem of understanding fundamental physical constants was discussed in particle physics, astronomy and cosmology. Here, I show that a new insight comes from condensed matter physics and liquid physics in particular: fundamental…
Coupled gyrostat low-order models (GLOMs) are energy-conserving cores of Galerkin-truncated fluid and geophysical systems, including Rayleigh-Benard convection and vorticity dynamics. A single gyrostat always possesses two quadratic…
A brief review of modeling and simulation methods for a study of polymers at interfaces is provided. When studying truly multiscale problems as provided by realistic polymer systems, coarse graining is practically unavoidable. In this…
We introduce a new variational characterization of Gaussian diffusion processes as minimum uncertainty states. We then define a variational method constrained by kinematics of diffusions and Schr\"{o}dinger dynamics to seek states of local…
Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…
Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as…
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…
The dynamics of a system composed of inelastic hard spheres or disks that are confined between two parallel vertically vibrating walls is studied (the vertical direction is defined as the direction perpendicular to the walls). The distance…
In the field of machine learning, comprehending the intricate training dynamics of neural networks poses a significant challenge. This paper explores the training dynamics of neural networks, particularly whether these dynamics can be…
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
Coarse-grained models are widely used to explain the effective behavior of partially observable physical systems with hidden degrees of freedom. Reduction procedures in state space typically disrupt Markovianity and a fluctuation relation…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms…
It is well-known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity dependent viscosity. This unphysical dependency violates the Galilean invariance and limits the…
Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantification and practical tractability. It excels at generative…
For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a…
We study the regularity and uniqueness of weak solutions of a degenerate parabolic equation, arising as the limit of a stochastic lattice model of self-propelled particles. The angle-average of the solution appears as a coefficient in the…