Abstract
We introduce Active Subspace Coarse-Graining (ASCG), an interpretable framework for systematic bottom-up coarse-graining trained from atomistic molecular dynamics simulations that simultaneously defines the coarse-grained mapping, effective interactions, and the equations of motion within one unified mathematical framework. We employ active subspace learning to identify linear projections of atomistic degrees of freedom that maximally describe gradients of the potential energy, yielding a reduced set of coarse-grained variables that capture the dominant collective motions across the potential of mean force. Effective coarse-grained forces and noise terms are obtained directly from the same projection, eliminating the need for separate parameterization schemes. We demonstrate the ASCG method on three biomolecules: dialanine, Trp-cage, and chignolin. We show that free energy surfaces are recapitulated with Jensen-Shannon divergences as low as 0.034 while eliminating all solvent degrees of freedom and reducing solute dimensionality by more than 90%. The ASCG trajectories are integrated with timesteps up to 100 fs, around four to ten times larger than those possible with conventional coarse-graining methods, while ASCG models remain accurate with as little as 100 ns of training data. These results establish ASCG as a robust, data-efficient approach for learning complete coarse-grained representations directly from molecular forces, while representing a departure from traditional particle-based models.