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When calibrating or trying to approximate the rough heston model by a neural network, why is it done according to the hurst parameter, the correlation, the volatility of volatility and the forward variance, when in the definition of the model, the speed of reversion, initial variance and the mean variance to which it reverts to are also parameters, why do we encapsulate these three in the forward variance ? is it equivalent ?

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Refer to the paper Perfect hedging in rough Heston models, there is a relation

$$ \lambda\theta^0(t) = D^{\alpha+1}(E[V_t]-V_0)+\lambda E[V_t] $$

After substituting this formula into the original rough heston model and letting $\lambda$ being zero, you fill find the right formula

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