Gianluca Gregori

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:

By performing an ensemble of molecular dynamics simulations, the model-dependent ionisation state is computed for strongly interacting systems self-consistently. This is accomplished through a free energy minimisation framework based on the technique of thermodynamic integration. To illustrate the method, two simple models applicable to partially ionised hydrogen plasma are presented in which pair potentials are employed between ions and neutral particles. Within the models, electrons are either bound in the hydrogen ground state or distributed in a uniform charge-neutralising background. Particular attention is given to the transition between atomic gas and ionised plasma, where the effect of neutral interactions is explored beyond commonly used models in the chemical picture. Furthermore, pressure ionisation is observed when short range repulsion effects are included between neutrals. The developed technique is general, and we discuss the applicability to a variety of molecular dynamics models for partially ionised warm dense matter.

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.