  A physical self-learning machine can be defined as a nonlinear dynamical
system that can be trained on data (similar to artificial neural networks), but
where the update of the internal degrees of freedom that serve as learnable
parameters happens autonomously. In this way, neither external processing and
feedback nor knowledge of (and control of) these internal degrees of freedom is
required. We introduce a general scheme for self-learning in any
time-reversible Hamiltonian system. We illustrate the training of such a
self-learning machine numerically for the case of coupled nonlinear wave
fields.
