應(yīng)yl7703永利官網(wǎng)邀請(qǐng)，中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院劉歆教授將于2024年7月12日舉辦線上學(xué)術(shù)報(bào)告。歡迎廣大師生參加。

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

時(shí)間：2024年7月12日9:00

騰訊會(huì)議ID：150202842 密碼：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.

報(bào)告人簡(jiǎn)介

劉歆，中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院“馮康首席研究員”，博士生導(dǎo)師，計(jì)算數(shù)學(xué)與科學(xué)工程計(jì)算研究所副所長(zhǎng)。劉歆2004年本科畢業(yè)于北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院；并于2009年在中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院獲得博士學(xué)位。主要研究方向包括流形優(yōu)化、分布式優(yōu)化及其在材料計(jì)算、大數(shù)據(jù)分析和機(jī)器學(xué)習(xí)等領(lǐng)域的應(yīng)用。劉歆分別于2016年，2021年和2023年獲得國(guó)家自然科學(xué)基金委優(yōu)秀青年科學(xué)基金項(xiàng)目、杰出青年科學(xué)基金項(xiàng)目和科技部重點(diǎn)專項(xiàng)的資助?，F(xiàn)擔(dān)任MPC, JCM, JIMO, APJOR等國(guó)內(nèi)外期刊編委，《中國(guó)科學(xué)·數(shù)學(xué)》（中英文）青年編委，《計(jì)算數(shù)學(xué)》副主編；中國(guó)科學(xué)院青年創(chuàng)新促進(jìn)會(huì)理事長(zhǎng)；中國(guó)運(yùn)籌學(xué)會(huì)常務(wù)理事；中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)會(huì)副秘書長(zhǎng)，中國(guó)數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)常務(wù)理事。

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2024年7月9日