Historically, predictive methods in Physics have relied on mathematical models that describe the evolution of systems in response to external stimuli and constraints, based on physical assumptions considered valid under certain hypotheses. However, recent advances in data collection have shifted predictive models from parametric regression approaches to model-free methods like Artificial Neural Networks (ANN) [1]. Despite challenges as high data requirements, computational costs, and interpretability and explainability, data-driven models are becoming increasingly relevant in predictive physics [2]. A promising approach is to integrate Physical Knowledge into data science models, enhancing the predictive capacity of ANNs by constraining their predictions to satisfy physical laws [3]. A particular idea in this framework is Physically Guided Neural Networks with Internal Variables (PGNNIV), which incorporates physical principles as constraints between neurons, allowing the ANN to predict the state of a physical system, and unravel its internal (and non-measurable) variables, directly from observable data [4]. In continuum physics, universal physical principles are often expressed through Partial Differential Equations (PDEs), while data is often provided as sets of images, which represent continuous spatial data. Thus, PGNNIV show significant potential, leveraging that the mathematical operators used in image processing can be extended to standard differential operators in continuum physics, allowing PGNNIV to predict the state of a physical system as well as to extract information on its structure as direct outputs of the ANN [5]. In this work, we extend the PGNNIV methodology to continuum problems, showing its predictive capacity to get the input-output relation in a physical system from a sufficiently large data set, as well as its unraveling ability to extract knowledge on the system internal structure. This is always performed considering the constraints imposed by Physics and using only observable variables. Our method demonstrates to be able to predict accurately the state of the system for different boundary conditions in a computationally cost-competitive manner, as well as to unveil heterogeneous, anisotropic and non-linear material structure. It is also able to distil material nature from unstructured data, inferring information about its microstructure from macroscopic data, and allowing downstream material characterization, leveraging Artificial