Related papers: Computing the Invariant Distribution of Randomly P…
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…
Ensuring the stability of power systems is gaining more attraction today than ever before, due to the rapid growth of uncertainties in load and renewable energy penetration. Lately, wide area measurement system-based centralized controlling…
We theoretically study reflection and transmission of light in a one-dimensional disordered phase-conjugating medium. Using an invariant imbedding approach a Fokker-Planck equation for the distribution of the probe light reflectance and…
The dynamical evolution of a neural network during training has been an incredibly fascinating subject of study. First principal derivation of generic evolution of variables in statistical physics systems has proved useful when used to…
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…
In this work, the primary goal is to establish rigorous connection between the Fokker-Planck equation of neural networks with its microscopic model: the diffusion-jump stochastic process that captures the mean field behavior of collections…
Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of…
Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and…
Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a…
The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical…
A Langevin equation is proposed to describe the transport of overdamped Brownian particles in a periodic rough potential and driven by an unbiased periodic force. The equation can be transformed into the Fokker-Planck equation by using the…
We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The…
The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…
Gibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Calculation of topological invariants for crystalline systems is well understood in reciprocal space, allowing for the topological classification of a wide spectrum of materials. In this work, we present a new technique based on the…
Voltage stability in modern power systems involves coupled dynamics across multiple time scales. Conventional methods based on time-scale separation or static stability margins may overlook instabilities caused by the coupling of slow and…
We present the Fokker-Planck equation (FPE) for an inhomogeneous medium with a position-dependent mass particle by making use of the Langevin equation, in the context of a generalized deformed derivative for an arbitrary deformation space…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…