Stochastic quasi-Newton molecular simulations

Area of Science:

• Computational Chemistry
• Materials Science
• Statistical Mechanics

Background:

• Stochastic quasi-Newton (S-QN) methods enable efficient configurational space sampling and thermodynamic consistency.
• Previous work demonstrated S-QN's effectiveness in 1D and 2D systems.
• Reducing computational and memory demands is crucial for exploiting S-QN's full potential in complex simulations.

Purpose of the Study:

• To introduce a novel, efficient factorized algorithm for determining the adaptive compound mobility matrix (B) in S-QN methods.
• To reduce the computational complexity from O(n^3) to O(n^2) per time step.
• To develop a limited-memory version of the algorithm for further efficiency gains.

Main Methods:

• Factorization of the mobility matrix B into JJ(T).
• Development of an efficient algorithm for updating the noise multiplier J.
• Implementation of a recursive update scheme for limited-memory usage, inspired by L-BFGS.

Main Results:

• The new factorized algorithm (FSU) reduces multiplications per time step from O(n^3) to O(n^2).
• The limited-memory factorized update (L-FSU) further reduces computational effort to O(n).
• Analysis of FSU and L-FSU performance on a multiscale system demonstrates their effectiveness in convergence and sampling.

Conclusions:

• The factorized and limited-memory algorithms significantly enhance the efficiency of S-QN methods.
• These advancements enable the simulation of complex, high-dimensional potential energy landscapes.
• The developed methods are crucial for ambitious applications like structure optimization and automated mode extraction.