By enforcing geometric consistency in autoencoders through tangent-bundle penalties, you can reduce errors in learned dynamical systems by 50-70%, making reduced models reliable for predicting rare events like molecular transitions.
This paper solves a key problem in learning reduced models of complex dynamical systems: how to build accurate low-dimensional simulators from high-dimensional data. The authors use geometric constraints from data covariance to train autoencoders that preserve the underlying manifold structure, enabling better prediction of long-term system behavior like transition times between metastable states.