25 citations · 47 across the 12 of their papers we have counts for
13 papers
A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivatives
Guozhi Dong, Michael Hintermüller, Kostas Papafitsoros
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…
A Parallel Technique for Multi-objective Bayesian Global Optimization: Using a Batch Selection of Probability of Improvement
Kaifeng Yang, Guozhi Dong, Michael Affenzeller
Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluat…
First-order conditions for the optimal control of learning-informed nonsmooth PDEs
Guozhi Dong, Michael Hintermüller, Kostas Papafitsoros +1
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 a…
Second-order flows for computing the ground states of rotating Bose-Einstein condensates
Haifan Chen, Guozhi Dong, Wei Liu +1
Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are co…
Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud
Guozhi Dong, Hailong Guo, Zuoqiang Shi
This paper is dedicated to the development of numerical analysis for high-order methods solving partial differential equations on scattered point clouds. We build a novel geometric…
Optimization with learning-informed differential equation constraints and its applications
Guozhi Dong, Michael Hintermueller, Kostas Papafitsoros
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization pro…
Superconvergence of differential structure for finite element methods on perturbed surface meshes
Guozhi Dong, Hailong Guo, Ting Guo
Superconvergence of differential structure on discretized surfaces is studied in this paper. The newly introduced geometric supercloseness provides us with a fundamental tool to pr…
A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging science
Guozhi Dong, Michael Hintermüller, Ye Zhang
Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired b…
Quantitative Magnetic Resonance Imaging: From Fingerprinting to Integrated Physics-Based Models
Guozhi Dong, Michael Hintermüller, Kostas Papafitsoros
Quantitative magnetic resonance imaging (qMRI) is concerned with estimating (in physical units) values of magnetic and tissue parameters e.g., relaxation times , , or pro…
Convergence Rates of First and Higher Order Dynamics for Solving Linear Ill-posed Problems
Radu Boţ, Guozhi Dong, Peter Elbau +1
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…
Parametric Polynomial Preserving Recovery on Manifolds
Guozhi Dong, Hailong Guo
This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require…
Nonlinear Flows for Displacement Correction and Applications in Tomography
Guozhi Dong, Otmar Scherzer
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.…
Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces
Guozhi Dong, Bert Juettler, Otmar Scherzer +1
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 analysi…