Geoenergy applications beyond hydrocarbons will play an essential role in accelerating the energy transition: Carbon capture and storage (CCS) is one of the most important approaches to mitigate CO2 emissions; approximately 50% of the energy consumed in the northern hemisphere is needed for heating and cooling, and the expanded use of geothermal energy could lead to significant CO2 reduction; the development of a hydrogen economy for power, transport, and production will rely on intermittent hydrogen storage in geological formations or salt caverns.
All these low-carbon geoenergy applications need bespoke reservoir modelling approaches to estimate available pore volumes for storage, capture how fluids with vastly different properties (e.g. hydrogen vs. hot water) interact with multi-scale geological heterogeneities, and quantify possible operational risks (e.g., early breakthrough of cold water during geothermal energy extraction) while accounting for the uncertainties inherent to geological formations.
This talk will explore how mathematical techniques could be adapted to overcome limitations in existing modelling approaches for low-carbon geoenergy applications. Such new modelling approaches should help to ensure that we design meaningful reservoir models that can provide reservoir performance forecasts with reliable uncertainty bounds, which are needed for new geoenergy applications to advance our transition to a low-carbon energy future.
Contatto:
alessio.fumagalli@polimi.it
Mathematical imaging has for decades been a powerful catalyst for new developments across the mathematical sciences. At its core lie fundamental questions about how information can be represented, reconstructed, and interpreted from incomplete, noisy, or indirect data. Addressing these questions has led to deep advances in areas such as functional and harmonic analysis, geometry, variational methods, inverse problems, partial differential equations, probability and statistics, and, more recently, learning theory. The resulting interplay between theory, computation, and applications has made imaging a uniquely fertile meeting point for pure and applied mathematics alike. Applications span an extraordinary range of domains, including biomedical and materials imaging, astronomy, environmental science, cultural heritage, and emerging technologies such as autonomous systems and data-driven diagnostics.
The rapid rise of artificial intelligence is now reshaping the landscape of imaging science once again. Data-driven approaches, in particular deep learning, have achieved remarkable empirical success in tasks such as reconstruction, segmentation, and synthesis. At the same time, their opaque nature and heavy reliance on data raise fundamental mathematical questions concerning stability, generalisation, interpretability, uncertainty quantification, and the incorporation of prior knowledge and physical constraints.
In this talk, I will present mathematical imaging as a continuing source of new mathematical ideas and challenges in the age of AI. I will highlight how modern approaches seek to blend data-driven models with structure, geometry, and physical principles, giving rise to novel analytical frameworks and computational paradigms. This perspective positions imaging not merely as an application area, but as a driver for the next generation of mathematical theory at the interface of analysis, computation, and learning.
This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
Contatti:
laura.sangalli@polimi.it
paola.antonietti@polimi.it
The pursuit of reliable and robust machine learning has become a central focus, with statistics and data science playing pivotal roles in its advancement. We explore connections between distributional robustness and causality, providing methodological insights to enhance the reliability of AI systems. We examine the broader implications of these concepts through a case study in digital health and conclude by emphasizing the importance of rigorous real-world validation of machine learning and AI algorithms.
Flow and transport processes in domains composed of a porous medium and an adjacent free-flow region appear in a wide range of industrial, bio-medical and environmental applications. Industrial applications range from flow in fuel cells to drying processes; possible bio-medical applications include the interplay of distribution processes in blood vessels and in the surrounding tissue. Applications in environmental systems include infiltration of overland flow during rainfall, groundwater contamination due to infiltrating pollutants and evaporation from soil.
One of the key challenges for coupled free flow and porous-medium flow arises from the fact that the overall effective behaviour depends strongly on interface processes that occur on small spatial scales (pore scale), although the overall system of interest is often too large to resolve these processes explicitly in detail. REV-scale models are usually not able to capture all the relevant physical processes for such coupled systems. For the accurate description of interface phenomena, it is therefore necessary to develop model concepts that combine information gained through pore-scale and REV-scale models.
The first part of the lecture includes the following items:
-an explanation of relevant processes of mass, momentum and energy transfer at the interface between a free-flow and a porous-media system;
-a presentation of conceptual models for coupled single-phase free flow and two-phase porous-medium flow with a detailed description of the models in the free flow and in the porous medium for the pore and REV scale;
-comparison studies to show the advantages and disadvantages in relation to classical approaches; the coupling concepts are discussed on the basis of different technical or environmental issues.
In the second part of the lecture I would very much like to discuss the results on the basis of various detailed use cases. These include e.g. aspects of soil evaporation, heat storage in porous media, self-cooling of turbines or the salinization of soils.
This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
Contatti:
paola.antonietti@polimi.it
