This work is a study of acoustic non-reciprocity exhibited by a passive one-dimensional linear waveguide incorporating two local strongly nonlinear, asymmetric gates. Two local nonlinear gates break the symmetry and linearity of the waveguide, yielding strong global non-reciprocal acoustics, in the way that extremely different acoustical responses occur depending on the side of application of harmonic excitation. To the authors' best knowledge that the present two-gated waveguide is capable of extremely high acoustic non-reciprocity, at a much higher level to what is reported by active or passive devices in the current literature; moreover, this extreme performance combines with acceptable levels of transmissibility in the desired direction of wave propagation. Machine learning is utilized for predictive design of this gated waveguide in terms of the measures of transmissibility and non-reciprocity, with the aim of reducing the required computational time for high-dimensional parameter space analysis. The study sheds new light into the physics of these media and considers the advantages and limitations of using neural networks to analyze this type of physical problems. In the predicted desirable parameter space for intense non-reciprocity, the maximum transmissibility reaches as much as 40%, and the transmitted energy from upstream to downstream varies up to nine orders of magnitude, depending on the direction of wave transmission. The machine learning tools along with the numerical methods of this work can inform predictive designs of practical non-reciprocal waveguides and acoustic metamaterials that incorporate local nonlinear gates. The current paper shows that combinations of nonlinear gates can lead to extremely high non-reciprocity while maintaining desired levels of transmissibility.