Symplectic encoders for physics-constrained variational dynamics inference.

Area of Science:

• Computational physics
• Machine learning for dynamics

Background:

• Standard variational autoencoders (VAEs) prioritize data compression over interpretability.
• Learning the dynamics of Multiple Degree of Freedom (MDOF) systems remains a challenge.

Purpose of the Study:

• To develop a novel variational autoencoder (VAE) incorporating physical constraints.
• To enable learning of MDOF dynamic system dynamics with enhanced interpretability.

Main Methods:

• A new encoder architecture based on Hamiltonian Neural Networks is proposed.
• Symplectic constraints are imposed on the a posteriori distribution.
• The model learns an energy-preserving latent representation.

Main Results:

• The proposed VAE demonstrates robust trajectory predictions even under noisy conditions.
• The model successfully learns an energy-preserving latent representation of dynamic systems.
• It offers improved interpretability of the latent space compared to standard VAEs.

Conclusions:

• This physics-informed neural network advances the application of VAEs for dynamic systems.
• The energy-preserving latent space provides valuable insights for engineering problems.
• The model enhances both prediction accuracy and interpretability in learning system dynamics.