Scientific Machine Learning (SciML) is the inclusion of physical knowledge in Machine Learning tools. By blending data and physical information, SciML constructs models that are data-efficient, interpretable and physically-consistent, through the introduction of inductive biases into neural network architectures. In contrast to purely black-box models, SciML approaches leverage domain knowledge to achieve robust generalization when data are noisy, incomplete or expensive to obtain. One such approach distinguishes between measurable and non-measurable variables, and to introduce physical constraints both at the architecture and the training level [1]. This approach, coined as Physically-Guided Neural Networks with Internal Variables (PGNNIV), naturally enables uncertainty propagation and supports transfer learning. We illustrate the performance of PGNNIV for unveiling nonlinear, heterogeneous and anisotropic features in material science without the prescription of specific constitutive equations between internal variables (Fig. 1a). In addition, PGNNIV demonstrates the ability to explicitly handle uncertainty, both by providing predictions with quantified reliability and by characterizing uncertainty at the constitutive level (Fig 1b). Finally, we present a Python library incorporating tensor calculus and algebra to deal with any SciML framework, designed to be compatible with automatic differentiation and modern GPU architectures while keeping the geometric structure of the underlying physical problems. Together, these contributions position PGNNIV as a flexible and principled framework for discovering physics-aware, uncertainty-informed models of complex material behavior. REFERENCES [1] Muñoz-Sierra, Rubén, Jacobo Ayensa-Jiménez, and Manuel Doblaré. "On the application of Physically-Guided Neural Networks with Internal Variables to Continuum Problems." Mechanics of Materials 205 (2025): 105317.