Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hierarchy between singular set, Pareto critical set and stable Pareto critical set, and can handle the problem of superposition of local Pareto fronts, occurring in the general nonconvex case. Furthermore, a quadratic convergence result in a suitable set-wise sense is proven and tested in a number of numerical examples.Comment: 29 pages, 12 figure

Optimisation of confinement in a fusion reactor using a nonlinear turbulence model

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A two-fold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity.Comment: 32 pages, 8 figures, accepted to JP

Online Identification of VLRA Battery Model Parameters Using Electrochemical Impedance Spectroscopy

This paper introduces the use of a new low-computation cost algorithm combining neural networks with the Nelder–Mead simplex method to monitor the variations of the parameters of a previously selected equivalent circuit calculated from Electrochemical Impedance Spectroscopy (EIS) corresponding to a series of battery aging experiments. These variations could be correlated with variations in the battery state over time and, therefore, identify or predict battery degradation patterns or failure modes. The authors have benchmarked four different Electrical Equivalent Circuit (EEC) parameter identification algorithms: plain neural network mapping EIS raw data to EEC parameters, Particle Swarm Optimization, Zview, and the proposed new one. In order to improve the prediction accuracy of the neural network, a data augmentation method has been proposed to improve the neural network training error. The proposed parameter identification algorithms have been compared and validated through real data obtained from a six-month aging test experiment carried out with a set of six commercial 80 Ah VLRA batteries under different cycling and temperature operation conditions.Special thanks should also be expressed to the Torres Quevedo (PTQ) 2019 Aid from the State Research Agency, within the framework of the State Program for the Promotion of Talent and its Employability in R + D + i, Ref. PTQ2019-010787/AEI/10.13039/501100011033

A task-based approach to parallel parametric linear programming solving, and application to polyhedral computations

Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type of parallel applications is challenging, because several tasks mightbe computing the same region. In this paper, we are presenting thealgorithm itself with a parallel redundancy elimination algorithm, andconducting a thorough performance analysis.Comment: arXiv admin note: text overlap with arXiv:1904.0607