Department of
Environmental Sciences, Informatics and Statistics

Applied Mathematics

The laboratory focuses on the development and application of efficient numerical schemes for the approximation, learning, control, and uncertainty quantification of complex phenomena governed by partial differential equations.
The main focuses are on the modelling of phenomena  in computational epidemiology, hydrology, and geosciences.

Research group

Contacts:
 gabriele.santin@unive.it
Tel.: +39 041 234 8517

Collaborations

Publications

For a complete list of publications, please visit the webpages of the members of the lab.

Research projects

  • Perturbation problems and asymptotics for elliptic differential equations

    In this project we consider perturbation and asymptotic problems for elliptic differential equations. We consider several different types of perturbation: domain (regular and singular perturbation for electromagnetic, degenerate, Steklov, nonlinear and higher order problems, corner singularities, etc.), mass and geometry (eigenvalue bounds and optimization), coefficients (regularity and stability, constant/nonconstant cases). The main aim of the project is to exploit the interplay between potential theory and calculus of variations and, on a higher scale, to involve more prominently geometric ideas in unprecedented ways: we will not only study perturbation and asymptotic problems in Riemannian settings, but also apply geometric techniques for the study of problems in Euclidean spaces. Apart from actual perturbation problems, we also consider more abstract, foundational questions that are necessary to improve the understanding of the geometrical and functional structure, such as: the role of the mass from a geometric point of view; domain perturbation in a general Riemannian setting; reducible operators for solving general BVPs; numerical computation of potentials; regularity properties of layer potentials; etc.

    Sito web: https://sites.google.com/uniroma1.it/pat/

  • HydroROM - Reduced order models of hydraulic protection systems for extreme water hazards

    PI: Antonia Larese (UNIPD); project PRIN22 2022PXYYK5 (28/09/2023 - 27/09/2025)

    Extreme hydrological events, such as floods and rock/debris or mud flows, are in rapid growth and this tendency will keep worsening in the near future. Our levees, dams, check dams, and flood control structures have mostly been conceived based on design criteria not adequate to the actual frequency and intensity of extreme hydrological events. This means that, in many cases, we cannot predict the response of an operating hydraulic structure to unforeseen events, preventing timely planning of adequate retrofitting intervention. The physical description of these hydraulic systems takes into account the mutual interaction between the fluid phase and the deformable boundary of the structures. The numerical simulation of these coupled systems is extremely computationally demanding, thus limiting the practical application of these numerical models. The goal of the project is the creation of Digital Twins (DTs) for hydraulic and protection structures under hydrological hazards such as floods and debris flows. The DT must be able to predict the structure response in real-time to adapt to the fast-flowing measurement data. The needed computational speed will be achieved combining Data Assimilation (DA) and Reduced Order Models (ROMs) to design machine learning techniques for complex and accurate high fidelity DTs. ROMs will capture the relevant features of the real process, while guaranteeing the computational efficiency for quasi real time applications. DAs will continuously correct and optimize the ROMs by the seamless flow of monitoring data during operational conditions.

  • Data-driven discovery and control of multi-scale interacting artificial agent systems

    The main goal of the project consists in developing sustainable and flexible next-generation frameworks for data-driven modelling, optimization, and simulation of multi-scale interacting agent systems of utmost importance in industrial applications and socio-economic life. As a scientific aim, we investigate several approaches relying on learning-based mathematical methods to build and control physical data-driven models. The proposal is timely since learning-based methods have recently attracted the attention of the scientific community to fully exploit HPC hardware and the abundance of data, demanding new unifying concepts to address grand challenges.

    Sito web: https://www.di.univr.it/?ent=progetto&id=5971&lang=en

  • EPIDOC - Epidemiological data assimilation and optimal control for short-term forecasting and emergency management of COVID-19 in Italy

    PI: Damiano Pasetto; project FISR 2020, EPIDOC_FISR_2020IP_04249 (26/07/2021 - 26/01/2022)

    The EPIDOC project will develop a reliable decision support system for short-term (1-3 weeks) prediction of the spatiotemporal spread of COVID-19 in Italy. The goal of the project is twofold: it will produce a platform that will automatically update the epidemiological forecast as soon as daily data become available (first phase) and evaluate the optimization of a portfolio of control actions to contain disease transmission (second phase). The model projections will be made directly accessible online on a dedicated platform. These goals will be achieved using a multidisciplinary approach that combines epidemiological modeling, dynamic systems analysis, numerical analysis, and optimization applied to estimation and control.

Last update: 25/03/2025