Machine learning techniques are used to predict values of fixed parameters when given reference values of critical parameters. For example, a neural network can be trained based on one or more critical parameters and a low-dimensional real-valued vector associated with a spectrum, such as a spectroscopic ellipsometry spectrum or a specular reflectance spectrum. Another neural network can map the low-dimensional real-valued vector. When using two neural networks, one neural network can be trained to map the spectra to the low-dimensional real-valued vector. Another neural network can be trained to predict the fixed parameter based on the critical parameters and the low-dimensional real-valued vector from the other neural network.