Advances in machine learning have expanded its application in engineering, with various models now being derived from data measurements. However, fundamental engineering principles remain well-established and effective across numerous applications. The machine learning approach in this proposal aims to enhance these physical models by incorporating data-driven corrections or augmentation, through modelling the discrepancy, which is the modelling error with respect to data measurements [1]. This work also focuses on creating explainable data augmentation by transforming model discrepancies into a sum of partial differential terms, making the results easier to interpret and understand, and useful in different engineering applications. To achieve the project’s objectives in a high-dimensional space, this work will leverage the domain decomposition technique, specifically PINN-PGD [2], to identify missing partial differential equation (PDE) terms. This approach augments the physical model, allowing for subsequent validation by solving the modified PDE. The method is showcased on a data originating from a nonlinear model, while the assumed known physical model is linear. The results showcase how the proposed technique complements the linear model with non-linear terms, to discover the original non-linear formulation. The proposed method can be used to characterize the deviations of the structural modeling of ships from physical measurements and enhance the original material modeling formulation.