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 Modelling, 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 modelling 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 Modelling, 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.
In the last fifty years computer simulations have increased their impact on research, design, production and are now an indispensable tool for development and innovation in science and technology. Partial Differential Equations (PDEs) offer a broad and flexible framework for modeling and analyzing a number of phenomena arising in fields as diverse as physics, engineering, biology, and medicine. Not surprisingly, research on methods to simulate PDEs has a central role in modern science.
IMATI has a long tradition in the study of PDEs that we address 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.
The research on numerical and theoretical aspects of PDEs (8 researchers) is the trademark of the institute with, in the last five years, two ERC Starting grants (BioSMA and GeoPDEs) and several recognitions as plenary talks, prizes, and an impressive publication record - about 90 publications (of which 5 highly cited papers), more than 400 cites. The group constantly attracts brilliant young researchers and visiting scholars.
Our research is currently developed following four main research axes:
- Discretization methods based on the use of splines.
- Discretization methods for PDEs on polygonal and polyhedral meshes.
- Non conforming domain decomposition methods.
- Systems of conservation laws and related topics.
Shape and Semantics Modelling
The research team, established by Bianca Falcidieno in the early 80s, was one of the first CNR groups focusing on Computer Graphics, legitimately included in the Computational Mathematics area, and core expertise of the research group. The research activity focuses on the variety of challenges related to the shape of 3D objects, ranging from the study of representation methods and of geometric analysis tools for 3D shape modeling, classification and recognition, to knowledge formalization about the shape and the context where it is embedded and used.
The group also performs research in Knowledge Management, including methods for semantic analysis and management of multi-dimensional data and, more generally, of web resources exposed following the Linked Data paradigm.
The foundational research in Shape and Semantics Modelling (S&SM) has application in a variety of contexts, such as cultural heritage, industrial production, geo-spatial and environmental data management, medicine, bioinformatics. In all these domains integrating geometric information with semantics plays a key role with respect to the growing demand for massive digitization. The excellence of the team is reflected by the high level scientific publications and by a strong participation in international projects (e.g. in FP7, H2020).
The expertise of the group attracts many national and international collaborations with research institutions and universities, mainly with an interdisciplinary nature, with researchers and students exchanges. Among others, we collaborate with Università di Genova (Mathematics, Engineering and Computer Science depts.) Università di Bologna ( Mathematics), RWTH-AAchen/Germany (geometry processing and mesh reparing), Univ. of Southern Australia (machine learning for functionality recognition), Univ. of New York at Stony Brook/US (numerical methods for 3D shape analysis), LIMOS and Univ. of Clermont Ferrand/France and AMPT in Aix en Provence (shape analysis). At regional level, the group is involved in the Research and Innovation Research Pole POLITECMED (Polo Ligure delle TECnologie MEDicali) and collaborates with local administrations and companies.
Thanks to capacity of attracting new funds and by investing in training of young researchers, the group is currently composed of 12 researchers and technologists, a senior researcher and 2 research directors; between 2012 and 2014 the group has supervised 12 Master theses and 6 Ph.D. theses and has supported 6 research fellows and 4 collaborators.
Computing Architectures and High Performance Computing
Thanks to the technological and scientific progresses, nowadays it is possible to acquire huge data set using sophisticated instruments and study large multidisciplinary problems through numerical models; this results in the need of high computational power as a means of gaining understanding of complex phenomena and insight into the data for a growing number of applications.
IMATI has a long tradition in the field of Computing Architectures and High Performance Computing. The main goal of this research is the study and development of methodologies and models for the effective and efficient exploitation of advanced computing systems in order to improve the quality of software for advanced applications. The research group working on these areas claims collaborations at national and international levels, and the participation to regional, national and EU scientific projects. The group also cooperates with Ligurian local authorities and small/medium enterprises through the promotion of technology transfer.
The diffusion of parallel and distributed computing puts the activity on Computing Architectures and High Performance Computing at the forefront of many initiatives. The highlight is on the achievements of three related FP7 projects: DRIHMS, DRIHM, DRIHM2US, aimed at the design and implementation of a research e-Infrastructure for hydro-meteorology studies of extreme events. The Italian Civil Protection, among the others, endorsed these results, promoting DRIHM as a candidate Italian e-Infrastructure. The research team is currently composed of 1 research director, 2 researchers, 2 postdocs, and 4 research grants. The research team has a considerable attractiveness to young researchers and students with different levels of maturity, in the last five years the group has supervised 4 Master theses, 2 PhD students, and 2 stages in the context of International collaborations.
Stochastic Modelling and Data Analysis
To understand real phenomena, the scientist almost invariably must deal with randomness. The increasing complexity of human activities on one side and the ability of collecting increasing amounts of data has made stochastic modelling and statistical data analysis essential disciplines for the representation of phenomena and knowledge extraction from data.
Since 1980 this group has specialized in probability and statistics, building expertise in space and time stochastic processes, stochastic differential equations and nonparametric methods. Traditionally the Bayesian inferential paradigm has been adopted, but the know-how of the group also includes other inferential approaches. Applications are a fundamental aspect of a statistician's work; at IMATI, stochastic modelling and data analysis have been applied to problems in industry, engineering, ecology, geophysics, finance and medicine.
The diversified competencies of the group have made it possible to successfully address a wide range of problems, which is demonstrated by numerous publication in international journals, by the participation to funded research projecs, regional projects, national flagship projects and EU projects with relevant technology transfer components, and by contracts with private companies. The group has a extended network of international contacts and it attracts visiting scholars and young researchers also from abroad. A trademark activity of the group is the annual Applied Bayesian Statistics school for the training of young researchers, taught by internationally recognized experts.
Our research is currently developed following thre main research axes: