Related papers: Decomposing force fields as flows on graphs recons…
We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…
Markov process is widely applied in almost all aspects of literature, especially important for understanding non-equilibrium processes. We introduce a decomposition to general Markov process in this paper. This decomposition decomposes the…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
Fluid deformation controls myriad processes in random flows including mixing and dispersion, stress development in complex fluids, colloid transport and deposition, droplet breakup and emulsification, fluid-structure interaction, chemical…
In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…
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…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…
Proton imaging is a powerful technique for imaging electromagnetic fields within an experimental volume, in which spatial variations in proton fluence are a result of deflections to proton trajectories due to interaction with the fields.…
Recent progress in the holographic approach makes it more transparent that each conductivity can be decomposed into the coherent contribution due to momentum relaxation and the incoherent contribution due to intrinsic current relaxation. In…
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…
A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…
By writing the flow equations for the continuum Legendre effective action (a.k.a. Helmholtz free energy) with respect to a particular form of smooth cutoff, and performing a derivative expansion up to some maximum order, a set of…
The study of Markov chains on discrete spaces, such as digraphs, has captivated mathematicians in recent decades due to its interconnectedness with topology, geometry, dynamics, spectral theory, and differential equations. Furthermore,…
We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one…
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena.…