Variance minimization variational Monte Carlo method

A variance-minimization scheme for optimizing Jastrow factors

We describe a new scheme for optimizing many-electron trial wave functions by minimizing the unreweighted variance of the energy using stochastic integration and correlated-sampling techniques. The scheme is restricted to parameters that are linear in the exponent of a Jastrow correlation factor, which are the most important parameters in the wave functions we use. The scheme is highly efficient and allows us to investigate the parameter space more closely than has been possible before. We search for multiple minima of the variance in the parameter space and compare the wave functions obtained…

Variational principles in quantum Monte Carlo: the troubled story of variance minimization

We investigate the use of different variational principles in quantum Monte Carlo, namely energy and variance minimization, prompted by the interest in the robust and accurate estimate of electronic excited states. For two prototypical, challenging molecules, we readily reach the accuracy of the best available reference excitation energies using energy minimization in a state-specific or state-average fashion for states of different or equal symmetry, respectively. On the other hand, in variance minimization, where the use of suitable functionals is expected to target specific states regardles…

Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization

We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study interacting driven diffusive systems where the efficiency…

基于变分能量最小化的神经网络密度泛函理论

Neural-network Density Functional Theory Based on Variational Energy Minimization

针对深度学习密度泛函理论依赖数据驱动监督学习、与DFT发展割裂的问题，本研究提出统一神经网络优化与DFT变分计算的理论框架，开发融合物理信息的可微分DFT代码，实现无监督学习，为该领域提供新范式。

量子系统神经变分蒙特卡洛中基于方差的收敛准则

A Variance-Based Convergence Criterion in Neural Variational Monte Carlo for Quantum Systems

本研究开发了一种以能量方差为收敛准则的轻量级通用神经变分蒙特卡洛求解器，验证了其在谐振子、氢原子等量子系统中的可靠性，并推导不等式明确了该方法在节点系统中的局限性。

密度矩阵最小化与ℓ1正则化

Density matrix minimization with $\ell_1$ regularization

本文提出了一种凸变分原理，用于寻找对称矩阵低能本征空间的稀疏表示，通过ℓ1正则化实现密度矩阵最小化，并证明了该算法收敛性。