Atomic-scale representation and statistical learning of tensorial properties

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule

Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte

Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments

Heat generation and transfer in automotive dry clutch engagement

Dynamic behaviour of automotive dry clutches depends on the frictional characteristics of the contact between the friction lining material, the flywheel, and the pressure plate during the clutch engagement process. During engagement due to high interfacial slip and relatively high contact pressures, generated friction gives rise to contact heat, which affects the material behaviour and the associated frictional characteristics. In practice excess interfacial slipping and generated heat during torque transmission can result in wear of the lining, thermal distortion of the friction disc, and reduced useful life of the clutch. This paper provides measurement of friction lining characteristics for dry clutches for new and worn state under representative operating conditions pertaining to interfacial slipping during clutch engagement, applied contact pressures, and generated temperatures. An analytical thermal partitioning network model of the clutch assembly, incorporating the flywheel, friction lining, and the pressure plate is presented, based upon the principle of conservation of energy. The results of the analysis show a higher coefficient of friction for the new lining material which reduces the extent of interfacial slipping during clutch engagement, thus reducing the frictional power loss and generated interfacial heating. The generated heat is removed less efficiently from worn lining. This might be affected by different factors observed such as the reduced lining thickness and the reduction of density of the material but mainly because of poorer thermal conductivity due to the depletion of copper particles in its microstructure as the result of wear. The study integrates frictional characteristics, microstructural composition, mechanisms of heat generation, effect of lining wear, and heat transfer in a fundamental manner, an approach not hitherto reported in literature

Stochastic Model Predictive Control for economic/environmental operation management of microgrids

Microgrids are subsystems of the distribution grid which comprises generation capacities, storage devices and controllable loads, which can operate either connected or isolated from the utility grid. In this work, microgrid management system is developed in a stochastic framework. Uncertainties due to fluctuating demand and generation from renewable energy sources are taken into account and a two-stage stochastic programming approach is applied to efficiently optimize microgrid operations while satisfying a time-varying request and operation constraints. Mathematically, the stochastic optimization problem is stated as a mixed-integer linear programming problem, which can be solved in an efficient way by using commercial solvers. The stochastic problem is incorporated in a Model Predictive Control (MPC) scheme to further compensate the uncertainty though the feedback mechanism. Simulations show the effective performance of the proposed approach