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Abstract Adhesive bonding of composite materials has become increasingly crucial for advanced engineering applications, offering unique advantages for lightweight and high-performance designs. This study presents a novel framework, physics-informed failure mode proportion prediction (PIFMP) model, for predicting failure mode proportions in composite adhesive joints, addressing critical gaps in understanding mixed-mode failure behaviors. In contrast to conventional approaches that focus solely on force or stress prediction, this research integrates important parameters from multistage manufacturing processes (MMPs) and simulation data into a physics-informed machine learning (PIML) framework, enabling proactive failure prediction and design optimization. The proposed framework unifies data-driven machine learning models with features derived from finite element analysis (FEA), incorporating cohesive zone modeling (CZM) to capture the physical dynamics of adhesive behavior under lap shearing. By embedding FEA-based physics features into the machine learning process and leveraging a time-series transformer model to analyze the temporal progression of interfacial damage and separation, the framework ensures predictive accuracy and physics-informed consistency, enabling precise analysis of failure mechanisms. The empirical study validates the effectiveness and the reliability of the framework, demonstrating enhanced predictive performance through cross-validation. The work establishes a foundational approach for failure analysis and provides a robust basis for future advancements. 

Low-dimensional and computationally less-expensive reduced-order models (ROMs) have been widely used to capture the dominant behaviors of high-4dimensional systems. An ROM can be obtained, using the well-known proper orthogonal decomposition (POD), by projecting the full-order model to a subspace spanned by modal basis modes that are learned from experimental, simulated, or observational data, i.e., training data. However, the optimal basis can change with the parameter settings. When an ROM, constructed using the POD basis obtained from training data, is applied to new parameter settings, the model often lacks robustness against the change of parameters in design, control, and other real-time operation problems. This paper proposes to use regression trees on Grassmann manifold to learn the mapping between parameters and POD bases that span the low-dimensional subspaces onto which full-order models are projected. Motivated by the observation that a subspace spanned by a POD basis can be viewed as a point in the Grassmann manifold, we propose to grow a tree by repeatedly splitting the tree node to maximize the Riemannian distance between the two subspaces spanned by the predicted POD bases on the left and right daughter nodes. Five numerical examples are presented to comprehensively demonstrate the performance of the proposed method, and compare the proposed tree-based method to the existing interpolation method for POD basis and the use of global POD basis. The results show that the proposed tree-based method is capable of establishing the mapping between parameters and POD bases, and thus adapt ROMs for new parameters.