Gianluca Gregori

Abstract:

Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of applicability. Perhaps the most successful and ubiquitous of these approaches is density functional theory (DFT). Its Kohn-Sham formulation has been the basis for many fundamental physical insights, and it has been successfully applied to fields as diverse as quantum chemistry, condensed matter and dense plasmas. Despite the progress made by DFT and related schemes, however, there remain many problems that are intractable for existing methods. In particular, many approaches face a huge computational barrier when modeling large numbers of coupled electrons and ions at finite temperature. Here, we address this shortfall with a new approach to modeling many-body quantum systems. Based on the Bohmian trajectories formalism, our new method treats the full particle dynamics with a considerable increase in computational speed. As a result, we are able to perform large-scale simulations of coupled electron-ion systems without employing the adiabatic Born-Oppenheimer approximation.

Abstract:

Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities, where similar simulated outputs can map back to very different sets of input parameters. While of fundamental importance, such instabilities are seldom resolved due to the intractably large number of simulations required to comprehensively explore parameter space. Here we show how Bayesian machine learning can be used to address inverse problem instabilities, and apply it to two popular experimental diagnostics in plasma physics. We find that the extraction of information from measurements simply on the basis of agreement with simulations is unreliable, and leads to a significant underestimation of uncertainties. We describe how to statistically quantify the effect of unstable inverse models, and describe an approach to experimental design that mitigates its impact.

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.