We investigate usage of nonlinear wave chaotic amorphous silicon (a-Si) cavities as physically unclonable functions (PUF). Machine learning attacks on integrated electronic PUFs have been demonstrated to be very effective at modeling PUF behavior. Such attacks on integrated a-Si photonic PUFs are investigated through application of algorithms including linear regression, k-nearest neighbor, decision tree ensembles (random forests and gradient boosted trees), and deep neural networks (DNNs). We found that DNNs performed the best among all the algorithms studied but still failed to completely break the a-Si PUF security which we quantify through a private information metric. Furthermore, machine learning resistance of a-Si PUFs were found to be directly related to the strength of their nonlinear response.