Gianluca Gregori

Abstract:

We present a machine learning based approach to address the study of transport processes, ubiquitous in continuous mechanics, with particular attention to those phenomena ruled by complex micro-physics, impractical to theoretical investigation, yet exhibiting emergent behavior describable by a closed mathematical expression. Our machine learning model, built using simple components and following a few well established practices, is capable of learning latent representations of the transport process substantially closer to the ground truth than expected from the nominal error characterising the data, leading to sound generalisation properties. This is demonstrated through an idealized study of the long standing problem of heat flux suppression under conditions relevant for fusion and cosmic plasmas. A simple analysis shows that the result applies beyond those case specific assumptions and that, in particular, the accuracy of the learned representation is controllable through knowledge of the data quality (error properties) and a suitable choice of the dataset size. While the learned representation can be used as a plug-in for numerical modeling purposes, it can also be leveraged with the above error analysis to obtain reliable mathematical expressions describing the transport mechanism and of great theoretical value.

Abstract:

We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background metric. We apply this method to the Robertson-Walker metric to derive a modified version of Friedmann's equations for a Universe consisting of scalar, spin-zero, massive particles. These modified equations include additional terms that result from the non-local nature of matter and appear as an acceleration in the expansion of the Universe. We see that the same effect may also be present in the case of an inhomogeneous expansion.

Abstract:

Proton radiography is a technique in high energy density science to diagnose magnetic and/or electric fields in a plasma by firing a proton beam and detecting its modulated intensity profile on a screen. Current approaches to retrieve the integrated field from the modulated intensity profile require the unmodulated beam intensity profile before the interaction, which is rarely available experimentally due to shot-to-shot variability. In this paper, we present a statistical method to retrieve the integrated field without needing to know the exact source profile. We apply our method to experimental data, showing the robustness of our approach. Our proposed technique allows not only for the retrieval of the path-integrated fields, but also of the statistical properties of the fields.