PhD program in Pure and Applied Mathematics (SmartData@PoliTO – UniTo)
PhD Student: Moreno Pintore
Context of the research activity
In many engineering applications uncertainty on data and models is becoming a relevant issue, and many techniques are under development in order to provide fast and reliable tools to perform uncertainty quantification analyses.
In several applications, the process under investigation requires performing simulations on a very complex model, or on a model affected by a large amount of uncertainty. Some situations also call for the sequential solution of well assessed models, but at different unknown scales or with unknown interactions.
When a large number of simulations for such models is required, deep learning can be a useful tool to investigate a wide range of configurations or parameter values. Furthermore, in recent works deep learning has been applied, in some contexts, to derive data driven models able to capture properties at different scales, or an unknown interaction between different phenomena, or to derive equivalent parameters via data driven homogeization techniques.
Several issues concerning the use of deep learning for these applications are still not sufficiently understood, and deserve a deep and wide investigation, as for example the choice of optimal learning sets, neural network performance testing and optimization.
The project is therefore multidisciplinary, as it involves several fields of investigation, in the framework of a specific engineering application: deep learning, numerical simulation, HPC techniques, optimization, statistics.
The research that the Ph.D. student will carry on will contribute to understand the role of Deep Learning in several engineering fields where simulations, complex models, and multi-scale phenomena play a fundamental role.
A topic which deserves investigation concerns the optimal construction of learning sets in order to conform to the statistical properties of the quantities of interest; their construction strategies and stabilization methods are also worth being analyzed. Quite often a trained neural network displays a very reliable behavior in predicting quantities of interest, but in some situations a large discrepancy between the actual quantities and those predicted by the neural network appears. It is worth investigating the possibility to perform some “a posteriori” rigorous or statistical (but also heuristic) analysis to detect and fix these discrepancies. The main field of interest for the research will be geophysics; in particular the study of fractured porous media with respect to the hydro-mechanical properties. For instance, the PhD student will apply deep learning techniques to analyze the possibility to predict underground flows depending on field probabilistic properties of fractures and porosity of the surrounding rock matrix, possibly considering several distributions of different pore scales. Results obtained could be applied to the same context, but to different phenomena (mechanical behaviour, fault slips, fault reactivation) or to different contexts with similar multi-scale heterogeneous nature. This research will be relevant in all applications related to underground resources exploitation (Oil&Gas, geothermal applications) or protection (water), or to geological storage (CO2, nuclear waste). In particular, the long term research will aim at contributing in providing reliable tools for risk evaluation.
Skills and competencies for the development of the activity
The candidate should have a good background in computer programming, mathematical modeling, numerical methods and statistics.
Further information about the PhD program at Politecnico can be found here
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