Accurate estimates of dynamical statistics using memory.

Area of Science:

• Computational chemistry
• Molecular dynamics
• Statistical mechanics

Background:

• Simulating long-timescale molecular processes is computationally challenging.
• Markov state models approximate dynamics as memoryless, potentially causing errors.
• Dynamical Galerkin approximation (DGA) offers an alternative but can also introduce systematic errors.

Purpose of the Study:

• To reformulate the dynamical Galerkin approximation (DGA) to incorporate memory effects.
• To improve the accuracy of estimating dynamical statistics for complex molecular systems.
• To reduce the computational cost and data requirements for kinetic analysis.

Main Methods:

• Developed a memory-aware reformulation of DGA inspired by quasi-Markov state models.
• Utilized the generalized master equation to encode projection-induced memory.
• Applied the method to a two-dimensional triple well potential and the AIB9 peptide system.

Main Results:

• The reformulated DGA successfully accounts for memory effects in dynamical approximations.
• Demonstrated robustness to the choice of basis functions.
• Achieved accurate kinetic predictions with an order of magnitude less time-series data.

Conclusions:

• The memory-aware DGA provides a more accurate and efficient approach for analyzing long-timescale molecular dynamics.
• This method mitigates systematic errors inherent in traditional Markovian approximations.
• Offers a significant advancement in computational approaches for chemical kinetics and molecular processes.