We present and experimentally evaluate the use of transfer learning to address experimental data scarcity when training neural network (NN) models for Mach-Zehnder interferometer mesh-based optical matrix multipliers. Our approach involves pretraining the model using synthetic data generated from a less accurate analytical model and fine-tuning it with experimental data. Our investigation demonstrates that this method yields significant reductions in modeling errors compared to using an analytical model or a standalone NN model when training data is limited. Utilizing regularization techniques and ensemble averaging, we achieve <1 dB root-mean-square error on the 3×3 matrix weights implemented by a photonic chip while using only 25% of the available data.