In the last few years, the research in mathematics and computer science for applications underwent a change in perspective. If, until recently, the different fields of mathematics were considered as separate research areas, nowadays the definition, the mathematical understanding and the computational solution of complex problems requires to jointly take into account a whole range of different aspects, and, therefore it demands a close interaction between the different relevant areas, ranging from statistics, to numerical analysis, to computer science.This idea drives the choices of many institutions which are at the forefront of the research in applied mathematics and computer science, from ICES (Texas) to Mathicse (EPFL), from INRIA (France) to MPI (Germany), and IMATI follows the same lines. The majority of IMATI researchers aim at facing problems arising from applications, by developing and using mathematical and computer science methodologies and by adapting them to the problem at hand. The expertise of IMATI researchers spans a large horizon with the following highlights:
Differential Modeling, with a special focus on partial differential equations considered from different points of view: theoretical (existence, uniqueness and regularity of the solutions), numerical (approximation schemes, stability and adaptivity) and computational (algorithms and computing methodologies). The results of these research programs are widely used to deal with problems raising from applications as, for instance, conservation laws, fluid dynamics, electromagnetics, semiconductor devices, non linear elastic and elasto-plastic materials, including shape memory alloys and rubber models.
Stochastic modeling and data analysis, with research programs focusing on the development and study of methodologies and models for the description of random phenomena, both in parametric and non-parametric frameworks. Applications cover engineering, seismology, biology, ecology, biomechanics, finance, health, decision making. The methodological approach is mostly, but not exclusively, Bayesian. Model classes are space and/or time stochastic processes and stochastic differential equations. Non-parametric techniques are also employed, such as non-parametric Bayesian models and classification methods.
Shape and Semantics Modeling, with research programs concerned with the study of all the aspects characterising the shape of 3D objects, ranging from geometry processing methods to the understanding of object functionality, up to the formalisation of knowledge and context of usage of multi-dimensional data and information. The interplay between geometry and semantics plays nowadays a central role in a large number of applications, ranging from established areas such as Product Manufacturing to Environmental Data management, Cultural Heritage and Medicine to cite a few. This research topic is a distinctive expertise of IMATI, with achievements of excellent results, strong international reputation and a lively and dynamic research group.
Computing Architectures and High Performance Computing, with research programs aiming at developing methodologies, algorithms, models and tools for an efficient and effective use of innovative heterogeneous complex computing architectures including both distributed and parallel systems. The design and implementation of distributed research infrastructures and of bio-info parallel algorithms are recent, well reputed activities in this field.
IMATI takes part intensively in both national and international research projects as main contractor and as partner. Besides the many European FP7 and H2020 projects that are active at the moment, IMATI is also involved in several actions at national and regional level, also with the aim of having an impact on the local production systems and SMEs. Moreover, IMATI is part of several national projects (e.g., "progetti premiali", flagship projects) and Italian technological clusters, showing its role within the CNR.