The multiscale coarse-graining method. VIII. Multiresolution hierarchical basis functions and basis function...

Area of Science:

• Computational Chemistry
• Molecular Modeling
• Statistical Mechanics

Background:

• The multiscale coarse-graining (MS-CG) method derives effective potentials for molecular models from atomistic simulations.
• Existing MS-CG methods face challenges with numerical stability and noise in determining these potentials.
• The coarse-grained potential is a variational approximation of the true many-body potential of mean force.

Purpose of the Study:

• To develop a new numerical algorithm for solving the MS-CG variational problem.
• To enhance numerical stability and suppress noise in the coarse-graining process.
• To enable the construction of accurate coarse-grained potentials for complex molecular systems.

Main Methods:

• A novel algorithm based on the elastic net method is proposed, incorporating noise suppression and enhanced numerical stability.
• A penalty parameter controls the selection of an optimal subset from a large basis set, preventing overfitting to simulation noise.
• New multiresolution basis functions, similar to Haar functions, are developed for improved differentiability in representing coarse-grained potentials.

Main Results:

• The proposed method demonstrates improved numerical stability and noise suppression for MS-CG variational problems.
• The elastic net variant effectively selects important basis functions, regularizing the linear least squares calculation and avoiding statistical error fitting.
• Feasibility is shown through a variational calculation of a coarse-grained potential, demonstrating the combined efficacy of the elastic net and new basis functions.

Conclusions:

• The new algorithm, combining elastic net regularization with multiresolution basis functions, significantly improves the MS-CG method.
• This approach allows for the use of very large basis sets in complex systems without numerical issues.
• It paves the way for more accurate and stable determination of coarse-grained potentials in molecular simulations.