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Hierarchical Machine Learning of Low-Resolution Coarse-Grained Free Energy Potentials.

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This study introduces a machine learning method for creating coarse-grained models, exploring how clustering affects free energy potentials. The approach efficiently builds hierarchical models without accuracy loss or increased computational cost.

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Area of Science:

  • Computational chemistry and materials science.
  • Machine learning and statistical mechanics.
  • Multiscale modeling and simulation.

Background:

  • Developing accurate coarse-grained (CG) models requires thermodynamically and statistically equivalent potentials to reference microscopic models.
  • Coarse-graining at supramolecular scales necessitates objective-oriented clustering of nonbonded particles, making the reduced description dependent on the clustering algorithm.
  • Existing methods for supervised machine learning (ML) of CG free energy (FE) potentials, like multiscale coarse-graining via force-matching (MSCG/FM), are efficient but can be influenced by clustering choices.

Purpose of the Study:

  • To explore the dependence of machine learning (ML) for coarse-grained (CG) Helmholtz free energy (FE) potentials on different clustering algorithms.
  • To develop a recursive ML methodology combining agglomerative clustering and MSCG/FM for efficient construction of fine-to-low resolution CG model hierarchies.
  • To demonstrate a method that avoids accuracy degradation and increased computational cost for larger hierarchies, removing upper size limitations for CG particles.

Main Methods:

  • Investigated the impact of partitional (k-means, Voronoi) and hierarchical agglomerative (bottom-up) clustering algorithms on ML-derived CG Helmholtz FE potentials.
  • Developed theoretical connections between the MSCG/FM learned potential and clustering statistics.
  • Proposed a recursive ML methodology integrating agglomerative clustering with MSCG/FM for hierarchical model development.
  • Demonstrated the methodology using all-atom molecular dynamics (MD) simulations of liquid nitromethane to obtain a bottom-up agglomerative hierarchy.

Main Results:

  • The ML of the CG Helmholtz FE potential is dependent on the chosen clustering algorithm.
  • A recursive methodology combining agglomerative clustering and MSCG/FM efficiently creates hierarchies of CG models without compromising accuracy or computational efficiency.
  • Renormalization group transformations were proven to exist for agglomerative hierarchies, indicating self-similarity and enabling low-cost learning of low-resolution potentials through rescaling.
  • The developed hierarchical CG models are suitable for constant-pressure simulations.

Conclusions:

  • The choice of clustering algorithm significantly influences the machine learning of coarse-grained free energy potentials.
  • A novel, efficient recursive machine learning methodology enables the construction of hierarchical coarse-grained models across multiple resolutions.
  • This approach facilitates the development of accurate, computationally tractable multiscale models for complex systems, including applications in constant-pressure simulations.