| Topic | People | Description |
|---|---|---|
| Stochastic partial differential equations and their applications |
Luca Di Persio
|
The research about (SPDEs and their applications spans a wide range of topics. With respect to theoretical contributions, we focus on fundamental aspects such as existence, uniqueness of solutions, invariant measures, and asymptotic expansions, with equations driven by general Lévy-type noises. Concerning applications, we consider mathematical finance problems exploiting SPDEs' methods to address challenges like option pricing under stochastic volatility, counterparty risk evaluation, and optimal execution strategies, often employing FBSPDEs and jump-diffusion models. Moreover, we consider control and optimization applications in memory-dependent systems, mean-field games, and stochastic control to manage uncertainty through dynamic programming and energy shaping. We also use SPDE techniques for electricity price forecasting, wind energy modelling, and control in robotics and teleoperation, emphasizing stochastic passivity and developing an innovative stochastic approach to port-Hamiltonian systems. Interdisciplinary applications extend to biomedicine, network dynamics, and interacting particle systems, showcasing the versatility of these mathematical tools in addressing complex problems in heterogeneous fields. |
| Problem solving in the context of artificial intelligence |
Luca Di Persio
|
The research fields covered by the Artificial Intelligence (AI) and Machine Learning we are interested in span various applications across finance, energy, and control systems. In finance, hybrid neural networks and deep learning are applied to forecasting, risk management, and investment optimization, including stock price prediction and volatility analysis. Energy systems benefit from AI-driven models for load forecasting, electricity price prediction, and renewable energy management. Stochastic control methods, enhanced by neural networks, address optimization challenges in dynamic and uncertain environments. Advanced neural architectures, such as recurrent networks and multitask learning, improve time series forecasting and domain-specific predictions. Interdisciplinary applications include biomedical engineering, where AI aids in analysing nanofluids, and robotics, where neural networks support motion control under stochastic dynamics. These studies emphasize the integration of AI to solve complex, high-impact problems. |
| Large scale interacting random systems |
Francesca Collet
Paolo Dai Pra |
This research field focuses on the study of complex systems composed of a large number of components that interact with each other according to probabilistic rules. The main goal is to understand how microscopic interactions give rise to the emergence of highly ordered or highly organized macroscopic collective behaviors, which are not easily predictable from the behavior of individual units. In more detail, the topics addressed include scaling limits, phase transitions, fluctuations, relaxation times, and applications to biology and social sciences. |
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