This thesis explores the development and application of data-driven machine learning and deep learning methods, together with physics-informed neural networks (PINNs), in the field of computational engineering. Motivated by the need for scalable, accurate, and interpretable models, especially in the presence of nonlinear and high-dimensional problems, the work addresses a broad range of applications including rough surface contact problems, beam mechanics, solid mechanics, and contact mechanics, covering both small and large deformation regimes. In the first part, a data-driven surrogate modeling framework is developed to predict the effective contact area in rough surface contact problems involving a linear elastic half-space and a rigid rough surface. Relying solely on statistical descriptors and far-field displacement inputs, several regression models are trained on data generated by computationally expensive boundary element method (BEM) simulations. The study identifies the Kernel Ridge model as offering the best trade-off between predictive accuracy, generalization capability, and computational efficiency. Despite the high cost of offline database generation, the resulting surrogate model demonstrates excellent performance for multi-query scenarios such as uncertainty quantification and sensitivity analysis, while also highlighting the limitations of black-box methods in terms of physical interpretability and extrapolation. To address the limitations of black-box models, the thesis transitions to physics-informed neural networks (PINNs), which incorporate governing equations and domain knowledge directly into the learning process. PINNs are applied to a wide spectrum of benchmark problems, ranging from linear elasticity and Euler-Bernoulli beam equations to contact mechanics with inequality constraints. In beam mechanics, challenges associated with high-order differential operators are addressed by successfully applying PINNs to static and dynamic beam problems, including nonlinear loading and variable cross-sections. In inverse problems, the issue of non-uniqueness is analyzed by attempting to identify unknown load distributions from partial displacement data. It is shown that the incorporation of prior physical knowledge significantly improves solution fidelity. For solid mechanics under small deformations, both displacement-based and mixed-variable PINN formulations are implemented and compared. Output transformations, particularly output scaling, are found to be essential for training stability and accuracy. These findings are validated on classical problems such as the Lam\'e test case and extended to high-dimensional setups including a 3D hollow sphere under time-dependent loading. For contact mechanics, which involve Karush-Kuhn-Tucker (KKT) constraints, various strategies are explored to enforce the KKT constraints, including sign-based, sigmoid-based, and Fischer-Burmeister formulations. These approaches are benchmarked against both analytical solutions and data-enhanced PINNs trained with FEM data, demonstrating the feasibility and limitations of PINNs in capturing complex contact behavior.In the context of large deformation problems, a novel element-based energy PINN (EBE-PINN) formulation is developed based on the principle of minimum potential energy. This formulation, inspired by finite element methodology, partitions the domain into subregions for more accurate and scalable integral evaluation. Hyperelastic Neo-Hookean materials are used to model nonlinear stress-strain relationships. Applications include 2D beam bending, 3D torsion of a square prism, and 3D contact problems such as the spherical contact problem and the torus instability example. EBE-PINNs are shown to be computationally competitive with FEM in training, and significantly faster during inference, making them a promising framework for nonlinear solid and contact mechanics simulations. Finally, the concept of hybrid digital twins is introduced to overcome the data limitations of purely deterministic or synthetic modeling approaches. A proof of concept is demonstrated using a steel-reinforced concrete beam, where real sensor data is integrated with PINN-based reduced-order models (ROMs). Both temporal and spatial surrogate modeling strategies are explored, and the models are benchmarked against analytical and purely data-driven alternatives. The results confirm that hybrid digital twins, when designed with appropriate physics and data coupling, provide flexible, interpretable, and accurate digital representations of physical systems.     «

This thesis explores the development and application of data-driven machine learning and deep learning methods, together with physics-informed neural networks (PINNs), in the field of computational engineering. Motivated by the need for scalable, accurate, and interpretable models, especially in the presence of nonlinear and high-dimensional problems, the work addresses a broad range of applications including rough surface contact problems, beam mechanics, solid mechanics, and contact mechanics,...     »