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In this work we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method is derived to approximate the solution of such differential models and we prove that it is…
This work presents a data-driven framework for multi-scale parametrization of velocity-dependent dispersive transport in porous media. Pore-scale flow and transport simulations are conducted on periodic pore geometries, and volume-averaging…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
A continuous time random walk (CTRW) model with waiting times following the Levy-stable distribution with exponential cut-off in equilibrium is a simple theoretical model giving rise to normal, yet non-Gaussian diffusion. The distribution…
Diffusion model deployment has been suffering from high energy consumption and inference latency despite its superior performance in visual generation tasks. Dynamic voltage and frequency scaling (DVFS) offers a promising solution to…
Elastic waves guided along bars of rectangular cross section exhibit complex dispersion. This paper studies in-plane modes propagating at low frequencies in thin isotropic rectangular waveguides through experiments and numerical…
We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and…
Embedding learning has found widespread applications in recommendation systems and natural language modeling, among other domains. To learn quality embeddings efficiently, adaptive learning rate algorithms have demonstrated superior…
Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
We present the Groupwise Diffusion Model (GDM), which divides data into multiple groups and diffuses one group at one time interval in the forward diffusion process. GDM generates data sequentially from one group at one time interval,…
The paper describes a distributed under-frequency load shedding and load restoration scheme, that exploits frequency and Rate-of-Change-of-Frequency (ROCOF) measurements produced by Phasor Measurement Units (PMUs) as detectors of a large…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We propose and validate a novel experimental technique to measure two-point statistics of turbulent flows. It consists in spreading rigid fibers in the flow and tracking their position and orientation in time and therefore been named…
Extragalactic Fast Radio Bursts (FRBs) have large dispersion measures (DMs) and are unique probes of intergalactic electron density fluctuations. By using the recently released First CHIME/FRB Catalog, we reexamined the structure function…
The diffusion model is used to calculate the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
In this paper we present a novel broadband approach for the extraction of dispersion curves of multiple time frequency overlapped dispersive modes such as in borehole acoustic data. The new approach works jointly in the Fourier and space…
A phenomenological model describing the time-frequency dependence of the power spectrum of thin plates vibrating in a wave turbulence regime, is introduced. The model equation contains as basic solutions the Rayleigh-Jeans equipartition of…
We present a methodology for the study of the dispersion of trajectories of stochastic processes in reconstructed phase spaces from observed data. The methodology allows to find ensembles of analog states, i.e. states that are close in the…