98 citations · 328 across the 15 of their papers we have counts for
16 papers
Hybrid Newton-BFGS high-index saddle dynamics for accelerating saddle-point searches
Jianyuan Yin, Lei Zhang, Shixue Zhang
We propose a hybrid Newton-BFGS high-index saddle dynamics (HiSD) method for accelerating saddle-point searches. The method constructs a Newton correction on the unstable subspace…
Subspace curvature-scaling high-index saddle dynamics for accelerating ill-conditioned saddle point searches
Jianyuan Yin, Lei Zhang, Zhiyi Zhang
We propose a subspace curvature-scaling high-index saddle dynamics (SCS-HiSD) method to accelerate high-index saddle dynamics (HiSD) for locating ill-conditioned saddle points. The…
A Geometry-Adaptive Deep Variational Framework for Phase Discovery in the Landau-Brazovskii Model
Yuchen Xie, Jianyuan Yin, Lei Zhang
The discovery of ordered structures in pattern-forming systems, such as the Landau-Brazovskii (LB) model, is often limited by the sensitivity of numerical solvers to the prescribed…
Convergence of high-index saddle dynamics for degenerate saddle points on critical manifolds
Tao Luo, Jianyuan Yin, Lei Zhang +1
The high-index saddle dynamics (HiSD) method provides a powerful framework for finding saddle points and constructing solution landscapes. While originally derived for nondegenerat…
Exploring transition pathways in the Landau-Brazovskii model
Zhiyi Zhang, Gang Cui, Kai Jiang +4
The Landau-Brazovskii model provides a theoretical framework for describing various phases arising from competing short- and long-range interactions in many physical systems. In th…
Learning task-specific predictive models for scientific computing
Jianyuan Yin, Qianxiao Li
We consider learning a predictive model to be subsequently used for a given downstream task (described by an algorithm) that requires access to the model evaluation. This task need…
Revealing Excited States of Rotational Bose-Einstein Condensates
Jianyuan Yin, Zhen Huang, Yongyong Cai +2
Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations. In this study, the ground and excited states of the rotational Bose-Einstein condens…
Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids
Baoming Shi, Yucen Han, Jianyuan Yin +2
We investigate critical points of a Landau-de Gennes (LdG) free energy in three-dimensional (3D) cuboids, that model nematic equilibria. We develop a hybrid saddle dynamics-based a…
Solution Landscapes of the Simplified Ericksen--Leslie Model and its Comparison with the Reduced Landau--de Gennes Model
Yucen Han, Jianyuan Yin, Yucheng Hu +2
We investigate the solution landscapes of a simplified Ericksen--Leslie (sEL) vector model for nematic liquid crystals, confined in a two-dimensional square domain with tangent bou…
Solution landscape of the Onsager model identifies non-axisymmetric critical points
Jianyuan Yin, Lei Zhang, Pingwen Zhang
We investigate critical points of the Onsager free-energy model on a sphere with different potential kernels, including the dipolar potential, the Maier-Saupe potential, the couple…
Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement
Zhen Xu, Yucen Han, Jianyuan Yin +3
We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta--Kawasaki model. The projected saddle…
Constrained high-index saddle dynamics for the solution landscape with equality constraints
Jianyuan Yin, Zhen Huang, Lei Zhang
We propose a constrained high-index saddle dynamics (CHiSD) method to search for index- saddle points of an energy functional subject to equality constraints. With Riemannian ma…
Transition pathways connecting crystals and quasicrystals
Jianyuan Yin, Kai Jiang, An-Chang Shi +2
Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here the nucleation of quasicrystals…
Solution landscape of a reduced Landau-de Gennes model on a hexagon
Yucen Han, Jianyuan Yin, Pingwen Zhang +2
We investigate the solution landscape of a reduced Landau--de Gennes model for nematic liquid crystals on a two-dimensional hexagon at a fixed temperature, as a function of ---t…
Searching the solution landscape by generalized high-index saddle dynamics
Jianyuan Yin, Bing Yu, Lei Zhang
We introduce a generalized numerical algorithm to construct the solution landscape, which is a pathway map consisting of all stationary points and their connections. Based on the h…
Construction of a pathway map on a complicated energy landscape
Jianyuan Yin, Yiwei Wang, Jeff Z. Y. Chen +2
How do we search for the entire family tree without unwanted random guesses, starting from a high-index and high-energy stationary state on the energy landscape? Here we introduce…