Complex, high-fidelity physical simulations can be computationally expensive due to a large number of degrees of freedom (DOF). In many cases, however, the physics driving these simulations couples the DOFs. This coupling creates an opportunity for reduced order models (ROMs) that can accurately predict a simulation’s future state using a smaller number of DOFs. A critical challenge of this approach, however, is embedding domain-specific properties into the ROM. In this talk, we discuss a recent extension of the LaSDI framework that is designed specifically for systems whose evolution is dictated by a second order time derivative. Our approach draws inspiration specifically from structural mechanics. Our method works by training an autoencoder to compress high-fidelity simulation data into a low dimensional latent representation while requiring the latent representation to evolve according to a learned differential equation whose left-hand-side is a second order time derivative. This restriction allows us to learn latent dynamics that obey the structure of the original system. We demonstrate the efficacy of this approach and its benefits over standard techniques, such as GP-LaSDI or SINDY Autoencoder.