Physics-Informed Neural Networks and Sequence Encoder: Application to heating and early cooling of thermo-stamping process

Abstract

In a previous work (Elaarabi et al., 2025b), the Sequence Encoder for online dynamical system identification (Elaarabi et al., 2025a) and its combination with PINN (PINN-SE) were introduced and tested on both synthetic and real data case scenarios. The sequence encoder is able to effectively encode time series into feature vectors, which the PINN then uses to map to dynamical behavior, predicting system response under changes in parameters, ICs and BCs. Previously (Elaarabi et al., 2025b), the tests on real data were limited to simple 1D problems and only 1D time series inputs of the Sequence Encoder. In this work, the possibility of applying PINN-SE to a more realistic case is investigated: heating and early cooling of the thermo-stamping process, which is a critical stage in the forming process of continuous fiber reinforced composite materials with thermoplastic polymer. The possibility of extending the PINN-SE inputs to multimodal data, such as sequences of temporal 2D images and to scenarios involving variable geometries, is also explored. The results show that combining multiple encoders with the previously proposed method (Elaarabi et al., 2025b) is feasible, we also show that training the model on synthetic data generated based on experimental data can help the model to generalize well for real experimental data, unseen during the training phase.

Figures (21)

• Figure 1: Overview of the setup used to validate PINN-SE. This setup includes the three main steps of the thermo-stamping process, focusing only on the thermal evolution. An IR camera is mounted in a fixed position above the mold using a support arm, while the mold is actuated using a hydraulic cylinder and controlled by a control unit. The steps can be summarized as follows: (a) The sheet is first heated to a certain temperature $T_h$ using an infrared (IR) oven. (b) The sheet is then taken out of the oven, where it is exposed to natural convection during the transfer phase. (c) Finally a cold mold is raised to establish thermal contact, emulating the cooling step of the stamping phase.
• Figure 2: Top view of the mold geometry and thermocouple positions.
• Figure 3: Top view of Temperature patterns after heating of the PA66GF and PPGF sheets of the samples used in these experiments.
• Figure 4: Top view of temperature patterns at the surface 15 seconds after contact with the mold of the PA66GF and PPGF sheets for all the samples used in this experiments.
• Figure 5: Illustration of heat transfer between two surfaces with asperities. The thermal contact resistance defines the quality of the contact and consequently the efficiency of heat transfer.