Flow-Matching: Efficient Coarse-Graining of Molecular Dynamics without Forces

Abstract

Coarse-grained (CG) molecular simulations have become a standard tool to study molecular processes on time and length scales inaccessible to all-atom simulations. Parametrizing CG force fields to match all-atom simulations has mainly relied on forcematching or relative entropy minimization, which require many samples from costly simulations with all-atom or CG resolutions, respectively. Here we present f low-matching, a new training method for CG force fields that combines the advantages of both methods by leveraging normalizing flows, a generative deep learning method. Flowmatching first trains a normalizing flow to represent the CG probability density, which is equivalent to minimizing the relative entropy without requiring iterative CG simulations. Subsequently, the flow generates samples and forces according to the learned distribution in order to train the desired CG free energy model via force-matching. Even without requiring forces from the all-atom simulations, flow-matching outperforms classical force-matching by an order of magnitude in terms of data efficiency and produces CG models that can capture the folding and unfolding transitions of small proteins.

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

“…When optimizing machine-learned force-fields with force matching, the noise contribution can dominate the force residual, 12,20 which leads to high variance and thus data inefficiency and a tendency to overfit. 59 The inherent flexibility in the choice of force mapping suggests that this situation can be improved by simply switching to a different force mapping scheme. We will therefore search for force maps that both satisfy the consistency relations in Eqs.…”

“…While these results apply to all force matched CG models, they are especially important for neural network CG potentials, which are sensitive to noise. 59 An open-source implementation of the proposed force mapping optimization is provided at https://github.com/noegroup/aggforce.…”

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

“…We also show that both high noise and constraint-inconsistent force mappings significantly degrade learned CG force fields. While these results apply to all force-matched CG models, they are especially important for neural network CG potentials, which are sensitive to noise . An open-source implementation of the proposed force mapping optimization is provided at .…”

“…The PMF error represents the bias and variance as a result of the limited expressivity of the CG model and finite data, while the noise is associated with the dimensionality reduction and represents the inherently stochastic nature of the mapped training forces from the perspective of the CG model. When machine-learned force fields are optimized with force matching, the noise contribution can dominate the force residual, , which leads to high variance and, thus, data inefficiency and a tendency to overfit . The inherent flexibility in the choice of force mapping suggests that this situation can be improved by simply switching to a different force mapping scheme.…”

“…While these results apply to all force-matched CG models, they are especially important for neural network CG potentials, which are sensitive to noise. 60 An open-source implementation of the proposed force mapping optimization is provided at https://github.com/ noegroup/aggforce.…”