Symplectic Encoders for Physics-Constrained Variational Dynamics Inference

We propose a new variational autoencoder (VAE) with physical constraints capable of learning the dynamics of Multiple Degreeof Freedom (MDOF) dynamic systems. Standard variational autoencoders place greater emphasis on compression thaninterpretability regarding the learned latent space. We propose a new type of encoder, based on the recently developedHamiltonian Neural Networks, to impose symplectic constraints on the inferred a posteriori distribution. In addition to deliveringrobust trajectory predictions under noisy conditions, our model is capable of learning an energy-preserving latent representationof the system. This offers new perspectives for the application of physics-informed neural networks on engineering problemslinked to dynamics.