  We present and experimentally evaluate using 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 pre-training the model using synthetic data generated from a less
accurate analytical model and fine-tuning 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 matrix weights
implemented by a 3x3 photonic chip while using only 25% of the available data.
