The demand for accurate and reliable numerical simulations of complex phenomena is increasing exponentially across a broad range of scientific and engineering applications. Problems like modeling fractal formation in macroscopic elasto-plasticity, simulation of biological systems, flow and transport in fractured formations are extremely challenging and require specific knowledge to be addressed.

Moreover, modeling becomes even more expensive when several different configurations or scenarios must be considered or when the object of the analysis must be optimized according to some criteria.

In addition, Machine and Deep Learning approaches (such as PINN, Deep Learning ROM, Auto-encoders just to name a few examples) are beginning to play an important role in advancing scientific discovery in several engineering domains, traditionally dominated by the numerical solution of PDEs.

To address the request for larger simulations, involving billions of unknowns, the development of novel and technology-aware algorithms able to exploit modern HPC systems is of paramount importance.