Related papers: Stochastic Optimal Prediction for the Kuramoto-Siv…
In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for controlled equation with delay in the state and with control dependent noise, in the general case of controls $u…
This paper is devoted to the study of the local rapid exponential stabilization problem for a controlled Kuramoto-Sivashinsky equation on a bounded interval. We build a feedback control law to force the solution of the closed-loop system to…
In this paper, we have studied the problem of determining the largest possible set of symmetries for an important example of nonlinear dynamical system: the Kuramoto-Sivashinsky (K-S) model in two spatial and one temporal dimensions. By…
A recent type of B-spline functions, namely trigonometric cubic B-splines, are adapted to the collocation method for the numerical solutions of the Kuramoto-Sivashinsky equation. Having only first and second order derivatives of the…
We propose an improved method for estimating partial differential equations and delay partial differential equations from data, using Bayesian optimization and the Bayesian information criterion to automatically find suitable…
In this paper, two boundary controllers are proposed to stabilize the origin of the nonlinear Kuramoto-Sivashinsky equation under intermittent measurements. More precisely, the spatial domain is divided into two sub-domains. The state of…
This paper studies the performative prediction problem which optimizes a stochastic loss function with data distribution that depends on the decision variable. We consider a setting where the agent(s) provides samples adapted to the…
Regression analysis with missing data is a long-standing and challenging problem, particularly when there are many missing variables with arbitrary missing patterns. Likelihood-based methods, although theoretically appealing, are often…
A defining characteristic of the Kadomstev-Petviashvili (KP) model equation is that the well-posedness results are subject to the restriction that at all transverse positions, the mass $\int u \,dx = \text{constant independent of $y$}.$ In…
We study the initial boundary value problem for one-dimensional Kuramoto-Sivashinsky equation with nonhomogeneous boundary conditions. Through the analysis of the boundary integral operator, and applying the known results on the Cauchy…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…
In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…
We present an equation-free multi-scale approach to the computational study of the collective dynamics of the Kuramoto model [{\it Chemical Oscillations, Waves, and Turbulence}, Springer-Verlag (1984)], a prototype model for coupled…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
We consider online statistical inference of constrained stochastic nonlinear optimization problems. We apply the Stochastic Sequential Quadratic Programming (StoSQP) method to solve these problems, which can be regarded as applying…
In this paper, we introduce an unbiased gradient simulation algorithms for solving convex optimization problem with stochastic function compositions. We show that the unbiased gradient generated from the algorithm has finite variance and…
Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…