The calibration of stochastic volatility and hybrid models to market smiles is a longstanding problem in quantitative finance. Partial answers have been given, for low-dimensional factor models such as old-fashioned one-factor local stochastic volatility (LSV) models or a hybrid Dupire local volatility model with a one-factor interest rate model, this calibration can be achieved by solving a two-dimensional non-linear Fokker-Planck partial differential equation (PDE) (Lipton, 2002). For multi