Augmenting Neural Differential Equations to Model Unknown Dynamical Systems with Incomplete State Information

Understand

Neural Ordinary Differential Equations replace the right-hand side of a conventional ODE with a neural net, which by virtue of the universal approximation theorem, can be trained to the representation of any function.

• When we do not know the function itself, but have state trajectories (time evolution) of the ODE system we can still train the neural net to learn the representation of the underlying but unknown ODE.
• However if the state of the system is incompletely known then the right-hand side of the ODE cannot be calculated.
• The derivatives to propagate the system are unavailable.