Related papers: A stochastic reduced-order model for statistical m…
In this paper we study second order stochastic differential equations with measurable and density-distribution dependent coefficients. Through establishing a maximum principle for kinetic Fokker-Planck-Kolmogorov equations with…
Phase-field modeling is an elegant and versatile computation tool to predict microstructure evolution in materials in the mesoscale regime. However, these simulations require rigorous numerical solutions of differential equations, which are…
This paper aims to investigate the non-Markovian dynamics. The governing equations are derived for the probability density functions (PDFs) of non-Markovian stochastic responses to Langevin equation excited by combined fractional Gaussian…
Using simulation to predict the mechanical behavior of heterogeneous materials has applications ranging from topology optimization to multi-scale structural analysis. However, full-fidelity simulation techniques such as Finite Element…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
Particle acceleration by turbulence plays a role in many astrophysical environments. The non- linear evolution of the underlying cosmic-ray spectrum is complex and can be described by a Fokker-Planck equation, which in general has to be…
Intracellular biomolecular systems exhibit intrinsic stochasticity due to low molecular copy numbers, leading to multimodal probability distributions that play a crucial role in probabilistic differentiation and cellular decision-making.…
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…
Fine-grained visual categorization (FGVC) is a challenging task due to similar visual appearances between various species. Previous studies always implicitly assume that the training and test data have the same underlying distributions, and…
In continuum robotics, real-time robust shape estimation is crucial for planning and control tasks that involve physical manipulation in complex environments. In this paper, we present a novel stochastic observer-based shape estimation…
In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations…
The description of Fermi acceleration developing in the phase-randomized simplified Fermi-Ulam model (SFUM) can be achieved in terms of a random walk taking place in momentum space. Within this framework the evolution of the probability…
Stochastic microstructure reconstruction involves digital generation of microstructures that match key statistics and characteristics of a (set of) target microstructure(s). This process enables computational analyses on ensembles of…
Stochastic differential equations play an important role in various applications when modeling systems that have either random perturbations or chaotic dynamics at faster time scales. The time evolution of the probability distribution of a…
Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid.…
In this paper, we consider stochastic versions of three classical growth models given by ordinary differential equations (ODEs). Indeed we use stochastic versions of Von Bertalanffy, Gompertz, and Logistic differential equations as models.…
Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the…
In this paper, we consider the density estimation problem associated with the stationary measure of ergodic It\^o diffusions from a discrete-time series that approximate the solutions of the stochastic differential equations. To take an…
A machine learning approach is presented to accelerate the computation of block polymer morphology evolution for large domains over long timescales. The strategy exploits the separation of characteristic times between coarse-grained…
The present report describes a big data numerical study of crystal plasticity finite element (CPFE) modelling using static and grain-based meshing to investigate the dependence of the results on the discretization approach. Static mesh…