Encoding prior knowledge in ensemble refinement.

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Data Analysis

Background:

• Analyzing noisy and incomplete data requires balancing experimental information with theoretical models.
• This trade-off is often viewed as a Pareto optimization problem, where improving agreement with experimental data can lead to inconsistencies with theoretical models.

Purpose of the Study:

• To propose a method for setting an 'exchange rate' a priori to balance the trade-off between experimental data and theoretical models.
• To introduce a framework for gentle ensemble refinement that properly balances experimental and theoretical information.

Main Methods:

• Focus on gentle ensemble refinement, where potential energy surface differences are small on a thermal scale.
• Relate the variance of energy differences to Kullback-Leibler divergence between Boltzmann distributions.
• Encode prior knowledge of energy uncertainties (force-field errors) into the exchange rate.

Main Results:

• The energy uncertainty is defined in the space of observables, depending on their type, number, and thermodynamic state.
• Demonstrate the relationship between gentle refinement and free energy perturbation theory.
• Show that encoding prior knowledge enhances the quality and transparency of ensemble refinement.

Conclusions:

• A balanced encoding of prior knowledge in ensemble refinement leads to improved quality and transparency.
• The findings extend to non-Boltzmann distributions, where energy uncertainty translates to information uncertainty.