We use artificial intelligence (AI) to learn and infer the physics of higher order gravitational wave modes of quasi-circular, spinning, non precessing binary black hole mergers. We trained AI models using 14 million waveforms, produced with the surrogate model NRHybSur3dq8, that include modes up to $\ell \leq 4$ and $(5,5)$, except for $(4,0)$ and $(4,1)$, that describe binaries with mass-ratios $q\leq8$ and individual spins $s^z_{\{1,2\}}\in[-0.8, 0.8]$. We use our AI models to obtain deterministic and probabilistic estimates of the mass-ratio, individual spins, effective spin, and inclination angle of numerical relativity waveforms that describe such signal manifold. Our studies indicate that AI provides informative estimates for these physical parameters. This work marks the first time AI is capable of characterizing this high-dimensional signal manifold. Our AI models were trained within 3.4 hours using distributed training on 256 nodes (1,536 NVIDIA V100 GPUs) in the Summit supercomputer.