This study presents a hybrid approach [2] that integrates the Proper Generalised Decomposition (PGD) [1] with deep learning techniques to develop real-time diagnostic and prognostic tools for clinicians, particularly in assessing compliance fields in fibrotic lungs. For these tools to be clinically relevant, they must be personalised, which requires numerical techniques capable of real-time estimation of patient-specific mechanical parameters. The proposed method mitigates the curse of dimensionality inherent in parametric problems by using a tensor decomposition. Each mode of the tensor decomposition is built upon the HiDeNN framework [3] and is therefore represented by a sparse neural network, with constrained weights and biases to replicate standard Finite Element Method (FEM) shape functions. This constraint enhances model interpretability and facilitates transfer learning, significantly accelerating the training process. Moreover, the model's architecture is directly determined by the mesh and the order of the interpolation, eliminating arbitrary choices and allowing mesh adaptation during the training stage. Similarly to PINNs, the physics of the problem is incorporated into the loss function during unsupervised training. The training process involves solving a minimisation problem, similar to classical model reduction. However, automatic differentiation within the neural network framework allows for greater flexibility in addressing non-linearities, particularly when linearisation is difficult. This tool therefore provides an ideal framework for building a patient-specific digital twin of human lungs. To achieve this, accounting for the shape variability of patients' organs is crucial. To that aim, the shapes of 40 patients were registered, meaning that the mapping between a generic spherical mesh and the shape of the patients' lungs was computed. From this mappings library, a shape model of the lung is built and can then be fed to the surrogate model of the lung.