Related papers: Artificial Neural Network Solver for Time-Dependen…
The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated solutions to the kinetic Fokker-Planck equation in a…
Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs for short) have been intensively investigated. In this paper we summarize some…
In this paper, we develop and analyze numerical methods for high dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a formulation of the Fokker-Planck equation as a system of…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. Despite the existence of…
Learning high-dimensional distributions is an important yet challenging problem in machine learning with applications in various domains. In this paper, we introduce new techniques to formulate the problem as solving Fokker-Planck equation…
We develop a new method to solve the Fokker-Planck or Kolmogorov's forward equation that governs the time evolution of the joint probability density function of a continuous-time stochastic nonlinear system. Numerical solution of this…
A numerical solution to the Fokker-Planck equation using a two-level scheme is presented. The Fokker-Planck (FP) equation is of parabolic type equation govern the time evolution of probability density function of the stochastic processes.…
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…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
Presenting a general phase approach to stochastic processes we analyze in particular the Fokker-Planck equation for the noisy Burgers equation and discuss the time dependent and stationary probability distributions. In one dimension we…
The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…
This study investigates the asymptotic dynamics of solutions to the Fokker-Planck-Kolmogorov (FPK) equation, with a specific focus on ship roll stability in dynamic sea conditions. Utilizing a fourth-order filter, we conduct a thorough…
The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and test a micro-macro version of parareal, in which the fine…
The aim of this contribution is to study the particle dynamics in a storage ring under the influence of noise. Some simplified stochastic beam dynamics problems are treated by solving the corresponding Fokker-Planck equations numerically.
An efficient method is presented as a means of an approximate, analytic time-dependent solution of the Fokker-Planck equation (FPE) for the Langevin model subjected to additive and multiplicative noise. We have assumed that the dynamical…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
We propose a new approach to constructing a neural network for predicting expectations of stochastic differential equations. The proposed method does not need data sets of inputs and outputs; instead, the information obtained from the…
Physics-informed neural networks are developed to characterize the state of dynamical systems in a random environment. The neural network approximates the probability density function (pdf) or the characteristic function (chf) of the state…
Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…