# Guozhi DongCentral South University | CSU · School of Mathematics and Statistics

Guozhi Dong

PhD, University of Vienna

## About

28

Publications

2,408

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65

Citations

Citations since 2016

## Publications

Publications (28)

We propose and analyze a numerical algorithm for solving a class of optimal control problems for learning-informed semilinear partial differential equations. The latter is a class of PDEs with constituents that are in principle unknown and are approximated by nonsmooth ReLU neural networks. We first show that a direct smoothing of the ReLU network...

Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to boost the execution time. An effective and straightforward approach is to design an acquisition function that...

Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to boost the execution time. An effective and straightforward approach is to design an acquisition function that...

In this paper we study the optimal control of a class of semilinear elliptic partial differential equations which have nonlinear constituents that are only accessible by data and are approximated by nonsmooth ReLU neural networks. The optimal control problem is studied in detail. In particular, the existence and uniqueness of the state equation are...

Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are considered to be first-order flows. This is a popular topic due to the recent advances of inertial dynamics with damping in convex optimization. Mathematically, the ground...

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems w...

Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-p...

A generic geometric error analysis framework for numerical solution of PDEs on sub-manifolds is established. It requires no global continuity on the patches, and also no embedding of the manifolds and tangential projections. This is different from the existing analysis in the literature, where geometry is assumed to be continuous and errors are mos...

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems w...

This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not ask for the tangent spaces of the exact manifolds which have been assumed for some significant gradient recovery methods in the literature. Another advantage of the proposed met...

This paper provides a general geometric condition for proving superconvergence of gradient recovery on deviated discretization of manifolds. It addresses open questions proposed by Wei,
Chen, and Huang in SIAM J. Numer. Anal., 48(2010), pp. 1920–1943. Two questions were asked there: (i) How to design gradient recovery algorithms given no exact info...

In this paper, we study damped second-order dynamics, which are quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems for accelerating energy decay of gradient flows. We concentrate on two equations: one is a damped second-order total variation flow, which is primari...

In this paper, we study damped second-order dynamics, which are quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems for accelerating energy decay of gradient flows. We concentrate on two equations: one is a damped second-order total variation flow, which is primari...

Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov's algorithm and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), respectively. In this paper we approach the solutions of linea...

Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov's algorithm and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), respectively. In this paper we approach the solutions of linea...

Quantitative magnetic resonance imaging (qMRI) is concerned with estimating (in physical units) values of magnetic and tissue parameters e.g., relaxation times T 1 , T 2 , or proton density ρ. Recently in [Ma et al., Nature, 2013], Magnetic Resonance Fingerprinting (MRF) was introduced as a technique being capable of simultaneously recovering such...

In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We show a preliminary convergence result of a relaxed convexification of the non-convex optimization problem. Some properties on the behavior of the solutions of these f...

Measuring the efficiency of Freight Villages (FVs) has important implications for logistics companies and other related companies as well as governments. In this paper we apply data envelopment analysis (DEA) to measure the efficiency of European FVs in a purely data-driven way, incorporating the nature of FVs as complex operations that use multipl...

In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We study properties of these filtering flows and provide experiments for correcting angular perturbations in tomographical data.

We study Tikhonov regularization for solving ill–posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account perturbations of the surfaces, in particular when the surfaces are approximated by spline surfaces. Another contribut...

We study regularization methods for solving ill--posed operator equations where the solutions are tangent vector fields. We review the classical regularization theory which applies to the infinite dimensional problem. In order to analyze the effect of approximations we extend the operator equation and spaces to ambient operators and spaces, respect...

In this paper we do a systematic investigation of continuous methods for pixel, line pixel and line dejittering. The basis for these investigations are the discrete line dejittering algorithm of Nikolova and the partial differential equation of Lenzen et al for pixel dejittering. To put these two different worlds in perspective we find infinite dim...

In this paper we do a systematic investigation of continu- ous methods for pixel, line pixel and line dejittering. The basis for these investigations are the discrete line dejittering algorithm of Nikolova and the partial differential equation of Lenzen et al for pixel dejittering. To put these two different worlds in perspective we find infinite d...

A typical task of image segmentation is to partition a given image into regions of homogeneous property. In this paper we focus on the problem of further detecting scales of discontinuities of the image. The approach uses a recently developed iterative numerical algorithm for minimizing the Mumford-Shah functional which is based on topological deri...

## Projects

Projects (3)

We study second order asymptotical regularization methods and its special numerical realization for abstract and concrete inverse problems.

Convergence Analysis of regularization methods, Gradient recovery on surfaces.