When Data Joins Physics More than a “Digital Twin” a new paradigm for simulation-based engineering

As models involved in science and engineering applications become too complex, their analytical solution is often compromised. However, computers are only able to perform very elementary operations efficiently.. Consequently, it is necessary to transform complex mathematical objects (derivatives, ...) into simpler objects, i.e. elementary operations, and at the same time, to reduce the number of points and time instants at which the solution of the model is evaluated (discretization). Such a procedure is known as numerical simulation and constitutes one of the three pillars of 20th century engineering modeling and experiments being the other two pillars. In the previous (third) industrial revolution, “virtual twins" (emulating a physical system by one, or more, mathematical models to describe its complex behaviour) were major protagonists. Nowadays, numerical simulation and modeling are present in most scientific fields and engineering domains, making accurate designs and virtual evaluation of systems responses possible drastically cutting the number of experimental tests.