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固定單元格體積下的晶體結構松弛的投影梯度下降算法

活動信息

  • 開始時間:2024-08-23 10:00:00
  • 活動地點:數學樓114
  • 主講人:劉歆

活動簡介

<p>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 detrminant constraint. Widely used line minimization-based methods 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. Moreover, it normally converges on all the systems, manifesting its unparalleled robustness. The results are consistent with the previous calculations and are further validated by experimental thermodynamic data.</p>

主講人介紹

劉歆,中國科學院數學與系統科學研究院“馮康首席研究員”,博士生導師,計算數學與科學工程計算研究所副所長。 劉歆2004年本科畢業于北京大學數學科學學院;并于2009年在中國科學院數學與系統科學研究院獲得博士學位。主要研究方向包括流形優化、分布式優化及其在材料計算、大數據分析和機器學習等領域的應用。劉歆分別于2016年,2021年和2023年獲得國家自然科學基金委優秀青年科學基金項目、杰出青年科學基金項目和科技部重點專項的資助。現擔任MPC, JCM, JIMO, APJOR等國內外期刊編委,《中國科學·數學》(中英文)青年編委,《計算數學》副主編;中國科學院青年創新促進會理事長;中國運籌學會常務理事;中國工業與應用數學會副秘書長,中國數學會計算數學分會常務理事。