Machine learning approach to the extended Hubbard model

The 1d extended Hubbard model with soft-shoulder potential has proved itself to be very difficult to study due its non solvability and to competition between terms of the Hamiltonian. Given this, we tried to investigate its phase diagram for filling n=2/5 and range of soft-shoulder potential r=2 by using Machine Learning techniques. That led to a rich phase diagram; calling U, V the parameters associated to the Hubbard potential and the soft-shoulder potential respectively, we found that for V<5 and U>3 the system is always in Tomonaga Luttinger Liquid phase, then becomes a Cluster Luttinger Liquid for 57, with a quasi-perfect crystal in the U<3V/2 and U>5 region. Finally we found that for U<5 and V>2-3 the system shall maintain the Cluster Luttinger Liquid structure, with a residual in-block single particle mobility.

ICE Emissions Estimation through Machine-learning techniques to support real-world R&D experiments

The emissions estimation, both during homologation and standard driving, is one of the new challenges that automotive industries have to face. The new European and American regulation will allow a lower and lower quantity of Carbon Monoxide emission and will require that all the vehicles have to be able to monitor their own pollutants production. Since numerical models are too computationally expensive and approximated, new solutions based on Machine Learning are replacing standard techniques. In this project we considered a real V12 Internal Combustion Engine to propose a novel approach pushing Random Forests to generate meaningful prediction also in extreme cases (extrapolation, very high frequency peaks, noisy instrumentation etc.). The present work proposes also a data preprocessing pipeline for strongly unbalanced datasets and a reinterpretation of the regression problem as a classification problem in a logarithmic quantized domain. Results have been evaluated for two different models representing a pure interpolation scenario (more standard) and an extrapolation scenario, to test the out of bounds robustness of the model. The employed metrics take into account different aspects which can affect the homologation procedure, so the final analysis will focus on combining all the specific performances together to obtain the overall conclusions.