  Inverse design has revolutionized the field of photonics, enabling automated
development of complex structures and geometries with unique functionalities
unmatched by classical design. However, the use of inverse design in nonlinear
photonics has been limited. In this work, we demonstrate quantum and classical
nonlinear light generation in silicon carbide nanophotonic inverse-designed
Fabry-P\'erot cavities. We achieve ultra-low reflector losses while targeting a
pre-specified anomalous dispersion to reach optical parametric oscillation. By
controlling dispersion through inverse design, we target a second-order
phase-matching condition to realize second- and third-order nonlinear light
generation in our devices, thereby extending stimulated parametric processes
into the visible spectrum. This first realization of computational optimization
for nonlinear light generation highlights the power of inverse design for
nonlinear optics, in particular when combined with highly nonlinear materials
such as silicon carbide.
