Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework Without Data

Abstract: Coarse-grained (CG) models offer an effective route to reducing the complexity of molecular simulations, yet conventional approaches depend heavily on long all-atom molecular dynamics (MD) trajectories to adequately sample configurational space. This data-driven dependence limits their accuracy and generalizability, as unvisited configurations remain excluded from the resulting CG model. We introduce a data-free generative framework for coarse-graining that directly targets the all-atom Boltzmann distribution. Our model defines a structured latent space comprising slow collective variables, which are statistically associated with multimodal marginal densities capturing metastable states, and fast variables, which represent the remaining degrees of freedom with simple, unimodal conditional distributions. A potentially learnable, bijective map from the full latent space to the all-atom configuration space enables automatic and accurate reconstruction of molecular structures. The model is trained using an energy-based objective that minimizes the reverse Kullback-Leibler divergence, relying solely on the interatomic potential rather than sampled trajectories. A tempering scheme is used to stabilize training and promote exploration of diverse configurations. Once trained, the model can generate unbiased, one-shot equilibrium all-atom samples. We validate the method on two synthetic systems-a double-well potential and a Gaussian mixture-as well as on the benchmark alanine dipeptide. The model captures all relevant modes of the Boltzmann distribution, accurately reconstructs atomic configurations, and learns physically meaningful coarse-grained representations, all without any simulation data.