Related papers: Time and space generalized diffusion equation on g…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
We study the Einstein relation between diffusion and response to an external field in systems showing superdiffusion. In particular, we investigate a continuous time Levy walk where the velocity remains constant for a time \tau, with…
Diffusion models have excelled in generating natural images and are now being adapted to a variety of data types, including graphs. However, conventional models often rely on Gaussian or categorical diffusion processes, which can struggle…
Flow of molecular gas into a complex vacuum system is investigated by a lumped parameter model to estimate the time evolution of gas pressure $p_g$, which for the first time takes into account the realistic effect of time-delay arising due…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…
The integration of Graph Neural Networks (GNNs) and Neural Ordinary and Partial Differential Equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their…
The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
We introduce graph gamma process (GGP) linear dynamical systems to model real-valued multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a…
We study transport in a one-dimensional lattice system with two conserved quantities -- `volume' and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
The generalised Boltzmann equation which treats the combined localised and delocalised nature of transport present in certain materials is extended to accommodate time-dependent fields. In particular, AC fields are shown to be a means to…
Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations. However, these methods are typically evaluated on benchmark…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
Anomalous dynamics in which local perturbations spread faster than diffusion are ubiquitously observed in the long-time behavior of a wide variety of systems. Here, the manner by which such systems evolve towards their asymptotic…
In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…
Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…