Invited review: Adaptive numerical modelling and hybrid physically based ANM approaches in materials engineering – a survey

Abstract

Many adaptive numerical modelling (ANM) techniques such as artificial neural networks (including multilayer perceptrons), support vector machines and Gaussian processes have now been applied to a wide range of regression and classification problems in materials science. Materials science offers a wide range of industrial applications and hence problem complexity levels from well physically characterised systems (e.g. high value, low volume products) to high volume low cost applications with intrinsic scatter due to commercial manufacturing processes. The authors review a number of recent examples in the literature, with the aim of identifying best practice in the use of these techniques as part of a multistrand modelling approach. The importance of understanding the basic principles of these modelling techniques and how they can link with other modelling strategies is emphasised. In particular the authors wish to identify the importance of hybrid physically based ANM in taking the field forward, which can range from, at the most basic level, careful data selection and data preprocessing to a full integration of physically based models with advanced ANM. A number of case studies are presented to illustrate the main points of the paper. Keywords: Neural networks, Support vector machines, Gaussian processes, Adaptive numerical modelling, Data driven techniques, Hybrid modelling, Applications in materials science IntroductionThe links between processing variables, microstructure evolution, resultant properties and hence mechanical performance are core tenets of materials engineering and a variety of modelling approaches have been applied to these materials modelling challenges. In some cases, a clear physical basis for such models has now been established, but often these can apply only to well defined conditions, which may not be representative of either genuine industrial (scaled up) production processes, or materials performance under realistic service conditions. The advantages of physically based models are:(i) they are robust to interpolation and extrapolation (as long as the underlying physical mechanisms being modelled are in operation) (ii) they should not require large amounts of data, as typically they only have a limited number of fitted parameters; ideally, a physically based model may have no fitted parameters (iii) the mechanistic verifications derived from physically based modelling may also offer insights into novel materials optimisation strategies (iv) a physically based model is relatively transparent, i.e. the mathematical underlying relationships between input and output parameters may be written in a reasonably clear mathematical form: this is part of a loosely defined group of methods which the authors term 'white box'. However, in a truly integrated processing-performance model, with the levels of uncertainty and complexity associated with industrial practice and complex service conditions, expressing these interlinked processes purely on physics based principles is unlikely to be feasible. ...

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