Three machine learning techniques (multilayer perceptron, random forest and Gaussian process) provide fast surrogate models for lower hybrid current drive (LHCD) simulations. A single GENRAY/CQL3D simulation without radial diffusion of fast electrons requires several minutes of wall-clock time to complete, which is acceptable for many purposes, but too slow for integrated modelling and real-time control applications. The machine learning models use a database of more than 16 000 GENRAY/CQL3D simulations for training, validation and testing. Latin hypercube sampling methods ensure that the database covers the range of nine input parameters ($n_{e0}$, $T_{e0}$, $I_p$, $B_t$, $R_0$, $n_{\|}$, $Z_{{\rm eff}}$, $V_{{\rm loop}}$ and $P_{{\rm LHCD}}$) with sufficient density in all regions of parameter space. The surrogate models reduce the inference time from minutes to $\sim$ms with high accuracy across the input parameter space.