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 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. For this reason, we aim to study these methods along three main directions organized in three main objectives:
MO1: Advanced computational and control methods for multi-scale agent systems
MO2: Intelligent particle methods in machine learning and inverse problems for large data
MO3: Artificial intelligence and data-driven models for socio-economic phenomena
In MO1 optimal control problems are investigated for interacting agent systems in a multi-scale framework. To break the “curse of dimensionality”, efficient numerical strategies are developed for the synthesis of feedback controls based on supervised-learning techniques and employing fast-stochastic algorithms for the simulation of state and adjoint dynamics. Applications of the derived methods are studied in the context of transportation systems (UAV, traffic, and pedestrian flow) to improve mobility and safety protocols. MO2 is focused on the derivation of learning and filtering methods based on interacting agent systems.
Innovative algorithms based on intelligent units able to cooperate to achieve a common goal are developed for the identification of uncertain systems and global optimization problems. Hence, these methodologies are used to obtain a substantial improvement in the speed-up of the training phase of machine learning problems, such as deep neural networks. Finally, data-driven models for applications in socio-economy and fast simulations are the core activity of MO3. Physics-informed neural networks (PINNs) are employed as an intelligence system for robust predictions of social dynamics, with particular emphasis on opinion formation in social media, wealth inequalities, and infectious disease emergence. Simultaneously, the improvement of HPC in terms of energy consumption is studied by modelling processor interactions with data from real supercomputers. In both directions, methodologies of MO1 and MO2, as well as model reduction techniques, will be of paramount importance to enhance the training phase of PINNs, and the performances of HPC architectures.
This is a project in collaboration with University of Ferrara, University of La Sapienza, Roma and University of Ca' Foscari, Venice.
