This paper uses neural network learning to identify learnable rational expectations equilibria in environments where equilibrium behaviour is indeterminate under rational expectations in some regions of the state space. The identified rational expectations equilibria acts as a source in locally indeterminate regions, meaning that endogenous variables are repelled and spend very little time in their neighbourhood. These results contrast sharply with the perfect-foresight behaviour in these environments, in which locally indeterminate regions act as a sink, attracting endogenous variables to their neighbourhood. Previous work has analysed such systems under perfect foresight or perturbation around steady states, discussing behaviour in the locally indeterminate region as acting as a sink. Such emphasis would appear to be misplaced, since under rational expectations the locally indeterminate region is a source not a sink. It is also shown that more familiar learning algorithms, such as recursive least square will converge to qualitatively similar equilibria, but the flexibility of a neural network is necessary for this equilibrium to be consistent with rational expectations. These results have potentially important implications in a wide range of contexts, as demonstrated by applying neural network learning to a simple New Keynesian model in which monetary policy is constrained by a Zero Lower Bound. If the indeterminacy due to this constraint on policy is bounded, agents can learn a fully-stochastic equilibrium with multiple steady states where transitory shocks can have permanent effects.