Material modelling has been for decades the centre of scientific efforts in the field of computational mechanics. A high number of parametric nonlinear families have been proposed for modelling elastic and inelastic solids. However, model selection and parameter identification and fitting are expensive and time consuming processes and frequently rely on data obtained under very specific and controlled lab tests.
At the era of data and the Internet of Things, data quantity is a more easily achievable requirement than data quality and science and technology have progressed to extract relevant information from available unstructured data using Machine Learning methods. In particular, Artificial Neural Networks are powerful tools to deal with nonlinearities provided that enough data are available, although they suffer from the inherent lack of explanatory capacity of “black-box” models.
We present the use of Physically-Guided Neural Networks with Internal Variables (PGNNIV) in computational mechanics. Due to their model-free character, there is no need of prescribing specific material models for predicting the system state under a given load. Indeed, the use of PGNNIV allows obtaining the material law as a by-product of the training process, that is performed using a training data-set of purely measurable variables (that is, only forces and displacements). The inclusion of physically meaningful constraints to deep neural networks endows the framework with explanatory capacity, placing the method within what is known as Explainable Artificial Intelligence (XAI).
The method is illustrated on a simple problem of nonlinear elasticity, showing good predictive and explanatory capacity while keeping low computational needs, something required in optimization and control scenarios. Then, a second application coming from biomedical engineering is presented, where a cell culture evolution problem is formulated in terms of some universal mass transport equations, that play the role of the universal conservation law, and some unknown constitutive relations associated with the cell metabolic activity, which in turn play the role of the material law. The framework presented shows again good predictive and explanatory capacities, thus taking the first steps in the direction of personalized medicine.