Machine Learning of Coarse-Grained Molecular Dynamics Force Fields

Abstract

Atomistic or ab initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force-matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multibody terms that emerge from the dimensionality reduction.

Machine Learning for Molecular Simulation

“…that is, the projection of the atomistic force ∇ x U on the collective variable space through the mapping E. In practice, the estimator (8) is very noisy: because of the dimensionality reduction from x to y, multiple realizations of the projected force f y lmf can be associated to the same value of the collective coordinates y and the minimum of the loss function (8) can not go to zero. By invoking statistical estimator theory it can be shown that this loss can be broken down into a bias, variance and noise terms [18].…”

“…Rather, it is about enforcing the correct asymptotic behavior of the energy when going towards an unphysical limit. CGnets proposed to achieve this by learning the difference to a simple prior energy that was defined to have the correct asymptotic behavior [18] (Fig. 5a).…”

“…Compared to the manual design of few-body free energy functionals, machinelearned free energies can help with transferability, as they are able to learn the important multi-body effects, e.g., to model neglected solvent molecules implicitly (Sec. 4.3) [16,17,18].…”

“…(17), and maximum likelihood, Eq. (18). For both, training and reweighting, we need to be able to compute the probability p X (x) of generating a configuration x.…”

“…iv) The same free energies as in i), ii), and iii) but as a function of only one reaction coordinate. Figures adapted from[18]. not necessary when using a deep neural network which automatically learns the required multi-body terms.…”