A new season for applied math

State of the art and perspectives

Applied mathematics is undergoing a period of further development thanks to the rise of disciplines which give again a new important role to the third pillar of scientific research, like numerical simulation, alongside theory and experiments.

Mathematical models of increasing complexity, which depend on a high number of parameters and are able to keep into account different scenarios and quantify uncertainties are requested in many different industrial fields, but also in environmental, biomedical and social sciences. These models allow the simulation of complex phenomena, processes but also simplify the design of products, by making applied mathematics an essential support for both theoretical and applied sciences thanks to its high level of interdisciplinarity, portability, and multidisciplinarity.

Processes related to innovation are in general supported by mathematical models which require an increasing complexity in order to simulate phenomena in a fast and yet accurate way. In this framework a new paradigm of applied mathematics require the support of the recent developments in

1. High Performance Computing (HPC) applied to numerical simulation for complex, multi-scale, and multiphysics simulations where a high number of parameters are involved;
2. data analysis for the assimilation of data obtained from the real world to be incorporated in mathematical models in order to minimise the distance between the mathematical model and the reality;
3. uncertainty quantification for the study of complex and mutable scenarios, many of these could not be known in advance;
4. model order reduction in order to reduce computational time and costs, but maintaining robustness and accuracy;
5. automatic learning approaches which provide an essential support for processes related to elaboration, optimisation, and analysis;
6. Digital Twins which now support full life of a real product with the aid of emerging technologies.
7. development of new numerical tools and computing technologies to explore further horizons in computational sciences

In this framework applied mathematics become an effective and versatile tool for facing up the challenges related to sustainability and for improving citizens’ life, for understanding climate changes, for protecting the environment, for improving working conditions and safety, for monitoring infrastructures, for analysing, and, at the same time, making the design, production and the maintenance more sustainable in different industrial fields, from transport to agri-food, from manufacturing to telecommunications.

Another field deserving a mention is the one related to biomedical applications, in which the main challenges reside in the complexity of the phenomena together with the morphological variability of the individuals: a mathematical model which depends on the individual (patient specific) and which can be built in real time for the simulation of the phenomenon of interest, able to model pathology on a potential patient, is one of the most ambitious horizon of applied mathematics and computational sciences in medical field.

SISSA mathLab group, celebrating these days the first 10 years of the research group, is actively pursuing the challenges described above in its everyday mission made up by educational initiatives in applied math, HPC, data science, and research also in cooperation with industries and hospitals, as well as outreach activities. More at http://mathlab.sissa.it.

In the subsequent stories you will have a better idea of our group activities and research fields and topics.