应兰州大学数学与统计学院邀请，中国科学院数学与系统科学研究院刘歆教授将于2024年7月12日举办线上学术报告。欢迎广大师生参加。

题目：Projected gradient descent algorithm for ab initio crystal structure relaxation under a fixed unit cell volume

时间：2024年7月12日9:00

腾讯会议ID：150202842 密码：2407

摘要：This talk is concerned with ab initio crystal structure relaxation under a fixed unit cell volume, which is a step in calculating the static equations of state and forms the basis of thermodynamic property calculations for materials. The task can be formulated as an energy minimization with a determinant constraint. Widely used line minimization-based methods (e.g., conjugate gradient method) lack both efficiency and convergence guarantees due to the nonconvex nature of the feasible region as well as the significant differences in the curvatures of the potential energy surface with respect to atomic and lattice components. To this end, we propose a projected gradient descent algorithm named PANBB. It is equipped with (i) search direction projections onto the tangent spaces of the nonconvex feasible region for lattice vectors, (ii) distinct curvature-aware initial trial step sizes for atomic and lattice updates, and (iii) a nonrestrictive line minimization criterion as the stopping rule for the inner loop. It can be proved that PANBB favors theoretical convergence to equilibrium states. Across a benchmark set containing 223 structures from various categories, PANBB achieves average speedup factors of approximately 1.41 and 1.45 over the conjugate gradient method and direct inversion in the iterative subspace implemented in off-the-shelf simulation software, respectively. Moreover, it normally converges on all the systems, manifesting its unparalleled robustness. As an application, we calculate the static equations of state for the high-entropy alloy AlCoCrFeNi, which remains elusive owing to 160 atoms representing both chemical and magnetic disorder and the strong local lattice distortion. The results are consistent with the previous calculations and are further validated by experimental thermodynamic data.

报告人简介

刘歆，中国科学院数学与系统科学研究院“冯康首席研究员”，博士生导师，计算数学与科学工程计算研究所副所长。刘歆2004年本科毕业于北京大学数学科学学院；并于2009年在中国科学院数学与系统科学研究院获得博士学位。主要研究方向包括流形优化、分布式优化及其在材料计算、大数据分析和机器学习等领域的应用。刘歆分别于2016年，2021年和2023年获得国家自然科学基金委优秀青年科学基金项目、杰出青年科学基金项目和科技部重点专项的资助。现担任MPC, JCM, JIMO, APJOR等国内外期刊编委，《中国科学·数学》（中英文）青年编委，《计算数学》副主编；中国科学院青年创新促进会理事长；中国运筹学会常务理事；中国工业与应用数学会副秘书长，中国数学会计算数学分会常务理事。

甘肃省高校应用数学与复杂系统省级重点实验室

甘肃应用数学中心

数学与统计学院

萃英学院

2024年7月9日