Related papers: Stochastic Optimal Prediction for the Kuramoto-Siv…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
This paper describes a new approach to solving some stochastic optimization problems for linear dynamic system with various parametric uncertainties. Proposed approach is based on application of tensor formalism for creation the…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
Consider the generalized Kuramoto-Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction-diffusion systems, to interface…
The Kuznetsov equation is a classical wave model of acoustics that incorporates quadratic gradient nonlinearities. When its strong damping vanishes, it undergoes a singular behavior change, switching from a parabolic-like to a hyperbolic…
In this paper we introduce a new methodology to determine an optimal coefficient of penalized functional regression. We assume the dependent, independent variables and the regression coefficients are functions of time and error dynamics…
We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…
When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have…
We prove existence of solutions to the Kuramoto-Sivashinsky equation with low-regularity data, in function spaces based on the Wiener algebra and in pseudomeasure spaces. In any spatial dimension, we allow the data to have its…
We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and…
This report provides an investigation into solving the Kuramoto-Sivashinsky equation in two spatial dimensions (2DKS) using a pseudo-spectral method on various rectangular periodic domains. The Kuramoto-Sivashinsky equation is a fluid…
We present a variational principle for the extraction of a time-dependent orthonormal basis from random realizations of transient systems. The optimality condition of the variational principle leads to a closed-form evolution equation for…
We present the global-in-time existence of strong solutions and its large-time behavior for the Kuramoto-Sakaguchi equation with inertia. The equation describes the evolution of the probability density function for a large ensemble of…
We consider data-driven reduced-order models of partial differential equations with shift equivariance. Shift-equivariant systems typically admit traveling solutions, and the main idea of our approach is to represent the solution in a…
This paper is concerned with the local output feedback stabilization of a nonlinear Kuramoto-Sivashinsky equation. The control is located at the boundary of the domain while the measurement is selected as a Neumann trace. This choice of…
Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…
Global well-posedness of the initial-boundary value problem for the stochastic Kuramoto-Sivashinsky equation in a bounded domain $D$ with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
In a separable Hilbert space, we study the minimization problem of a convex smooth function with Lipschitz continuous gradient whose evaluations are corrupted by random noise. To this end, we associate a stochastic inertial system that…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…