A Convolutional‑Neural‑Network Surrogate for Steady‑State Radiative Heating in Thermoforming

Abstract

Thermoforming is widely used to produce lightweight packaging and durable components, yet controlling the temperature field during the heating stage remains challenging. Finite‑element models that capture conduction, convection and diffuse‑radiative exchange provide accurate predictions, but their high computational cost precludes real‑time optimization and digital‑twin deployment. In this study a convolutional‑neural‑network (CNN) surrogate is developed to predict steady‑state temperature distributions for a polymer sheet heated by an array of radiative heaters. A parametric study sampled heater temperature distributions, sheet thicknesses and initial temperatures, and a nonlinear finite‑element model was discretized and used to compute steady‑state temperature fields. The resulting dataset of input vectors and temperature maps served to train a fully convolutional neural network, whose weights were optimized with the Adam algorithm by minimizing the mean‑squared error. On a held‑out test set the surrogate achieved a coefficient of determination of 0.96 and a mean relative error less than 3%, while producing predictions in under 1 second—an order‑of‑magnitude speedup relative to the finite‑element solver. Gradient‑based inversion of the trained network successfully recovered heater temperature distributions that reproduced target temperature fields, even under simulated heater failures, demonstrating the feasibility of fault‑tolerant control. These results show that the proposed CNN surrogate bridges high‑fidelity simulation and real‑time control, enabling digital‑twin implementations for thermoforming and providing a foundation for future extensions to transient heating and experimental validation.