What's Next? Predicting Hamiltonian Dynamics from Discrete Observations of a Vector Field

We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively evaluate the methods and observe that information that the system is Hamiltonian can be effectively informed, and that different methods strike different trade-offs between efficiency and effectiveness for different dynamical systems.

Recognizing three-dimensional phase images with deep learning

Optical phase contains key information for biomedical and astronomical imaging. However, it is often obscured by layers of heterogeneous and scattering media, which render optical phase imaging at different depths an utmost challenge. Limited by the memory effect, current methods for phase imaging in strong scattering media are inapplicable to retrieving phases at different depths. To address this challenge, we developed a speckle three-dimensional reconstruction network (STRN) to recognize phase objects behind scattering media, which circumvents the limitations of memory effect. From the single-shot, reference-free and scanning-free speckle pattern input, STRN distinguishes depth-resolving quantitative phase information with high fidelity. Our results promise broad applications in biomedical tomography and endoscopy.