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pro vyhledávání: '"LIU, Hailiang"'
We present a natural framework for constructing energy-stable time discretization schemes. By leveraging the Onsager principle, we demonstrate its efficacy in formulating partial differential equation models for diverse gradient flow systems. Further
Externí odkaz:
http://arxiv.org/abs/2406.12652
This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker-Planck equations, which admit a gradient flow structure and find application in diverse contexts. The solutions, representing density
Externí odkaz:
http://arxiv.org/abs/2403.15643
In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy for solving both the Cahn-Hilliard equation and the Allen-Cahn equation.
Externí odkaz:
http://arxiv.org/abs/2402.02712
Autor:
Huo, Xiaokai, Liu, Hailiang
Solving high dimensional partial differential equations (PDEs) has historically posed a considerable challenge when utilizing conventional numerical methods, such as those involving domain meshes. Recent advancements in the field have seen the emerge
Externí odkaz:
http://arxiv.org/abs/2401.17233
Extracting physical laws from observation data is a central challenge in many diverse areas of science and engineering. We propose Optimal Control Neural Networks (OCN) to learn the laws of vector fields in dynamical systems, with no assumption on th
Externí odkaz:
http://arxiv.org/abs/2312.01165
Neural networks with wide layers have attracted significant attention due to their equivalence to Gaussian processes, enabling perfect fitting of training data while maintaining generalization performance, known as benign overfitting. However, existi
Externí odkaz:
http://arxiv.org/abs/2310.10767
We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied to address the constraints in optimization problems, such as the Hessi
Externí odkaz:
http://arxiv.org/abs/2310.06733
Autor:
Bhatnagar, Manas, Liu, Hailiang
We review the theoretical development in the study of critical thresholds for hyperbolic balance laws. The emphasis is on two classes of systems: Euler-Poisson-alignment (EPA) systems and hyperbolic relaxation systems. We start with an introduction t
Externí odkaz:
http://arxiv.org/abs/2302.12869
Autor:
Bhatnagar, Manas, Liu, Hailiang
The Euler-Poisson system describes the dynamic behavior of many important physical flows including charge transport, plasma with collision and cosmological waves. We prove sharp threshold conditions for the global existence/finite-time-breakdown of s
Externí odkaz:
http://arxiv.org/abs/2302.04428
Anderson acceleration (AA) as an efficient technique for speeding up the convergence of fixed-point iterations may be designed for accelerating an optimization method. We propose a novel optimization algorithm by adapting Anderson acceleration to the
Externí odkaz:
http://arxiv.org/abs/2211.08578