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

arXiv cs.AI / 3/30/2026

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Key Points

The paper revisits the previously introduced Sequence Encoder with Physics-Informed Neural Networks (PINN-SE) for online dynamical system identification and prediction under changing parameters, initial conditions, and boundary conditions.
It extends evaluation from earlier limited 1D real-data tests to a more realistic thermo-stamping application, focusing on heating and early cooling behavior in continuous fiber reinforced composite forming.
The authors investigate expanding PINN-SE inputs beyond 1D time series to multimodal data, including sequences of temporal 2D images and cases with variable geometries.
Results indicate that using multiple encoders with the earlier method is feasible and that training on synthetic data generated from experimental measurements improves generalization to real experimental data not seen during training.

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.