Related papers: Data-driven computation for periodic stochastic di…
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…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…
An $N$-dimensional nonlinear Fokker-Planck equation is investigated here by considering the time dependence of the coefficients, where drift-controlled and source terms are present. We exhibit the exact solution based on the generalized…
The large time dynamics of a periodically driven Fokker-Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete…
This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and play an important role in quantifying propagation and evolution of uncertainty. Although Fokker-Planck equations can be written…
We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues…
Data-centric prognostics is beneficial to improve the reliability and safety of proton exchange membrane fuel cell (PEMFC). For the prognostics of PEMFC operating under dynamic load, the challenges come from extracting degradation features,…
This note provides an introduction to molecular dynamics, the computational implementation of the theory of statistical physics. The discussion is focused on the properties of Langevin dynamics, a degenerate stochastic differential equation…
We develop a tractable and flexible approach for incorporating side information into dynamic optimization under uncertainty. The proposed framework uses predictive machine learning methods (such as $k$-nearest neighbors, kernel regression,…
The energy system is rapidly changing to accommodate the increasing number of renewable generators and the general transition towards a more sustainable future. Simultaneously, business models and market designs evolve, affecting power-grid…
This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation…
Data-driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data-driven stochastic control. In this…
The paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control…
We present a data-driven approach to use the Koopman generator for prediction and optimal control of control-affine stochastic systems. We provide a novel conceptual approach and a proof-of-principle for the determination of optimal control…
The Fokker-Planck equations for stochastic dynamical systems, with non-Gaussian $\alpha-$stable symmetric L\'evy motions, have a nonlocal or fractional Laplacian term. This nonlocality is the manifestation of the effect of non-Gaussian…
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…
In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman-Bucy…
The auxiliary function method allows computation of extremal long-time averages of functions of dynamical variables in autonomous nonlinear ordinary differential equations via convex optimization. For dynamical systems defined by autonomous…