New Neural Flow Model Predicts Dissipative Hamiltonian Dynamics

A new machine learning model, CoSynFlow, has been developed to tackle the complex problem of predicting the behavior of dissipative Hamiltonian systems. Unlike many existing neural operator methods that prioritize prediction accuracy, CoSynFlow explicitly enforces the geometric structure of the dynamics, which is crucial for systems where energy is lost over time. The model achieves this by preserving the conformal symplectic structure, a mathematical property that describes how the system's state evolves. CoSynFlow combines symplectic shear maps with conformal scaling, allowing it to learn continuous-time solution maps. A key innovation is its ability to be conditioned on a finite-dimensional Hamiltonian descriptor and a dissipation parameter, enabling a single trained model to predict outcomes for entirely new systems without requiring further training. This approach maintains structure error at machine precision and delivers superior long-horizon prediction accuracy.