Coarse graining molecular dynamics with graph neural networks

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at an atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proved that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features to machine learn the force field. In the present contribution, we build upon the advance of Wang et al. and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learn their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning CG force-fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force-field on average. We show that there is flexibility in how to map all-atom forces to the CG representation, and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force-fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins Chignolin and Tryptophan Cage and published as open-source code.Comment: 44 pages, 19 figure

Coarse-Graining Auto-Encoders for Molecular Dynamics

Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and spatial scales involved in thermodynamic and kinetic phenomena in materials, atomistic simulations are often computationally unfeasible. Coarse-graining methods allow simulating larger systems, by reducing the dimensionality of the simulation, and propagating longer timesteps, by averaging out fast motions. Coarse-graining involves two coupled learning problems; defining the mapping from an all-atom to a reduced representation, and the parametrization of a Hamiltonian over coarse-grained coordinates. Multiple statistical mechanics approaches have addressed the latter, but the former is generally a hand-tuned process based on chemical intuition. Here we present Autograin, an optimization framework based on auto-encoders to learn both tasks simultaneously. Autograin is trained to learn the optimal mapping between all-atom and reduced representation, using the reconstruction loss to facilitate the learning of coarse-grained variables. In addition, a force-matching method is applied to variationally determine the coarse-grained potential energy function. This procedure is tested on a number of model systems including single-molecule and bulk-phase periodic simulations.Comment: 8 pages, 6 figure

Coarse-Graining with Equivariant Neural Networks: A Path Towards Accurate and Data-Efficient Models

Machine learning has recently entered into the mainstream of coarse-grained (CG) molecular modeling and simulation. While a variety of methods for incorporating deep learning into these models exist, many of them involve training neural networks to act directly as the CG force field. This has several benefits, the most significant of which is accuracy. Neural networks can inherently incorporate multi-body effects during the calculation of CG forces, and a well-trained neural network force field outperforms pairwise basis sets generated from essentially any methodology. However, this comes at a significant cost. First, these models are typically slower than pairwise force fields even when accounting for specialized hardware which accelerates the training and integration of such networks. The second, and the focus of this paper, is the need for the considerable amount of data needed to train such force fields. It is common to use tens of microseconds of molecular dynamics data to train a single CG model, which approaches the point of eliminating the CG models usefulness in the first place. As we investigate in this work, it is apparent that this data-hunger trap from neural networks for predicting molecular energies and forces is caused in large part by the difficulty in learning force equivariance, i.e., the fact that force vectors should rotate while maintaining their magnitude in response to an equivalent rotation of the system. We demonstrate that for CG water, networks that inherently incorporate this equivariance into their embedding can produce functional models using datasets as small as a single frame of reference data, which networks without inherent symmetry equivariance cannot

Differentiable molecular simulation can learn all the parameters in a coarse-grained force field for proteins

Finding optimal parameters for force fields used in molecular simulation is a challenging and time-consuming task, partly due to the difficulty of tuning multiple parameters at once. Automatic differentiation presents a general solution: run a simulation, obtain gradients of a loss function with respect to all the parameters, and use these to improve the force field. This approach takes advantage of the deep learning revolution whilst retaining the interpretability and efficiency of existing force fields. We demonstrate that this is possible by parameterising a simple coarse-grained force field for proteins, based on training simulations of up to 2,000 steps learning to keep the native structure stable. The learned potential matches chemical knowledge and PDB data, can fold and reproduce the dynamics of small proteins, and shows ability in protein design and model scoring applications. Problems in applying differentiable molecular simulation to all-atom models of proteins are discussed along with possible solutions and the variety of available loss functions. The learned potential, simulation scripts and training code are made available at https://github.com/psipred/cgdms