Deep Neural Networks with Symplectic Preservation Properties
This work addresses the challenge of maintaining symplectic properties in machine learning models for Hamiltonian systems, which is incremental as it adapts existing normalizing flow techniques to this domain.
The authors tackled the problem of learning unknown Hamiltonian systems while preserving symplectic structure by proposing a deep neural network architecture that outputs an invertible symplectomorphism, drawing an analogy to real NVP methods in normalizing flows.
We propose a deep neural network architecture designed such that its output forms an invertible symplectomorphism of the input. This design draws an analogy to the real-valued non-volume-preserving (real NVP) method used in normalizing flow techniques. Utilizing this neural network type allows for learning tasks on unknown Hamiltonian systems without breaking the inherent symplectic structure of the phase space.