Learning Physics Constrained Dynamics Using Autoencoders

We consider the problem of estimating states (e.g., position and velocity) and physical parameters (e.g., friction, elasticity) from a sequence of observations when provided a dynamic equation that describes the behavior of the system. The dynamic equation can arise from first principles (e.g., Newton's laws) and provide useful cues for learning, but its physical parameters are unknown. To address this problem, we propose a model that estimates states and physical parameters of the system using two main components. First, an autoencoder compresses a sequence of observations (e.g., sensor measurements, pixel images) into a sequence for the state representation that is consistent with physics by including a simulation of the dynamic equation. Second, an estimator is coupled with the autoencoder to predict the values of the physical parameters. We also theoretically and empirically show that using Fourier feature mappings improves the generalization of the estimator in predicting physical parameters compared to raw state sequences when learning from high-frequency data. In our experiments on three visual and one sensor measurement tasks, our model imposes interpretability on latent states and achieves improved generalization performance for long-term prediction of system dynamics over state-of-the-art baselines.