Many glass products require thermoformed geometry with high precision. However, the traditional approach of developing a thermoforming process through trials and errors can cause large waste of time and resources and often end up with unsuccessfulness. Hence, there is a need to develop an efficient predictive model, replacing the costly simulations or experiments, to assist the design of precision glass thermoforming. In this work, we report a surrogate model, based on a dimensionless back-propagation neural network (BPNN), that can adequately predict the form errors and thus compensate for these errors in mold design using geometric features and process parameters as inputs. Our trials with simulation and industrial data indicate that the surrogate model can predict forming errors with adequate accuracy. Although perception errors (mold designers' decisions) and mold fabrication errors make the industrial training data less reliable than simulation data, our preliminary training and testing results still achieved a reasonable consistency with industrial data, suggesting that the surrogate models are directly implementable in the glass-manufacturing industry.