Structure-Constrained Koopman Generators for Flexible Time-Stride Molecular Dynamics Simulations

Trajectory-based models can accelerate molecular dynamics (MD) simulations by predicting configurations over long temporal strides, but most are tied to a single prescribed temporal resolution during training, limiting their ability to leverage heterogeneous trajectory datasets and to infer dynamics at unseen time strides. To this end, we introduce FlexMD, a continuous-time Koopman framework that enables flexible time-stride prediction via structure-constrained equivariant latent dynamics. It encodes molecular configurations into an E(3)-invariant latent space and evolves them with a constrained linear generator. The generator preserves a learned quadratic invariant that regularizes latent evolution and prevents exponential amplification of error with positive definite matrix. The closed-form propagation of latent dynamics via matrix exponential enables a single model to learn across multiple temporal strides and perform inference at flexible temporal resolutions without iterative latent-space integration. We evaluate our method across various benchmarking datasets, including MD17, AdK, ATLAS, MD-CATH, and PET-MAD. Crucially, our model achieves accurate and stable long-horizon simulation, supports flexible inference across substantial training-test stride gaps, and benefits from multi-stride training that robustly improves generalization across temporal resolutions. These results demonstrate that the structure-constrained Koopman generator offers a principled and scalable path toward reliable long-timescale molecular simulation.