国产a片

荔园学者Colloquium第一百六十七期

讲座题目：Momentum Stability and Adaptive Control in Stochastic Reconfiguration

主讲人：刘歆 研究员（中国科学院数学与系统科学研究院）

讲座时间：2026年5月14日10:00-11:00

讲座地点：国产a片 粤海校区汇星楼四号教室

内容摘要：Variational Monte Carlo (VMC) combined with expressive neural network wavefunctions has become a powerful route to high-accuracy ground-state calculations, yet its practical success hinges on efficient and stable wavefunction optimization. While stochastic reconfiguration (SR) provides a geometry-aware preconditioner motivated by imaginary-time evolution, its Kaczmarzinspired variant, subsampled projected-increment natural gradient descent (SPRING), achieves state-of-the-art empirical performance. However, the effectiveness of SPRING is highly sensitive to the choice of a momentum-like parameter μ. The origin of this sensitivity and the instability observed at μ = 1 have remained unclear. In this work, we clarify the distinct mechanisms governing the regimes μ < 1 and μ = 1. We establish convergence guarantees for 0 ≤ μ < 1 under mild assumptions, and construct counterexamples showing that μ = 1 can induce divergence via uncontrolled growth along kernel-related directions when the step-size is not summable. Motivated by this theoretical insight and extensive numerical experiments, we further propose a tuning-free adaptive strategy for selecting μ based on spectral flatness and subspace overlap. This approach achieves performance comparable to optimally tuned SPRING, while significantly improving robustness in VMC optimization.

主讲人简介：刘歆，中国科学院数学与系统科学研究院研究员，博士生导师，计算数学与科学工程计算研究所副所长。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。2024年获得中国工业与应用数学学会萧树铁应用数学奖。现担任MPC, JCM, 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；中国工业与应用数学学会秘书长；中国运筹学会常务理事；中国数学会计算数学分会常务理事。

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　　　　　　　　　　　　　　　　　　　　 2026年5月8日