Physics-Informed Neural Networks for material modelling

Soft self-healing polymers have gained increasing attention due to their potential to enhance durability, sustainability, and safety in applications such as soft robotics, flexible electronics, and adaptive structures. However, modelling their mechanical behaviour it remains challenging because of strong nonlinearities, temperature dependence, and the coupling between molecular design parameters and the macroscopic response. In particular, inferring synthesis-related material parameters from mechanical data constitutes a complex inverse problem that is difficult to address using conventional constitutive modelling alone. This work investigates the use of machine learning techniques, specifically Data-driven Neural Networks and Physics-Informed Neural Networks (PINNs), for the inverse modelling of soft self-healing polymer networks based on Diels–Alder reversible chemistry. An experimental database of uniaxial stress–strain curves is constructed and used to train neural network models aimed at predicting key material parameters, namely the molar mass of the furan-functionalized chains, the stoichiometric ratio between reactive groups, and the furan functionality. A purely Data-driven Neural Network is first developed as a baseline model to assess the feasibility of parameter prediction from mechanical response data alone. To improve robustness, physical consistency, and generalization, a physics-informed approach is subsequently introduced. The PINN framework incorporates established continuum mechanics relations, based on a compressible neo-Hookean formulation and rubber elasticity theory, directly into the training process. This hybrid strategy constrains the learning task using physical laws, reducing ambiguity in parameter identification and mitigating overfitting in data-scarce regimes. The performance of the Data-driven and Physics-informed models is evaluated using quantitative error metrics and qualitative stress–strain curve comparisons. The results demonstrate that PINNs provide improved prediction accuracy, enhanced physical consistency, and greater stability compared to purely data-driven models. Overall, this work highlights the potential of physics-informed machine learning as an effective tool for material characterization and design, offering a promising pathway toward accelerated development of soft and self-healing polymer systems.