  We introduce a methodology for seeking conservation laws within a Hamiltonian
dynamical system, which we term ``neural deflation''. Inspired by deflation
methods for steady states of dynamical systems, we propose to {iteratively}
train a number of neural networks to minimize a regularized loss function
accounting for the necessity of conserved quantities to be {\it in involution}
and enforcing functional independence thereof consistently in the
infinite-sample limit. The method is applied to a series of integrable and
non-integrable lattice differential-difference equations. In the former, the
predicted number of conservation laws extensively grows with the number of
degrees of freedom, while for the latter, it generically stops at a threshold
related to the number of conserved quantities in the system. This data-driven
tool could prove valuable in assessing a model's conserved quantities and its
potential integrability.
