The Art and Craft of Data-Based Mechanistic (DBM) Modelling, Forecasting and Control
This is the title of my new book, due to be published by Springer Nature sometime in 2026. Although I first used the term ‘data-based mechanistic modelling’ in 1993, the basic concepts of this DBM approach to modelling dynamic systems were developed over many years prior to this. For example, they were first applied seriously within a hydrological context in the early 1970s, with application to the modelling of water quality and flow in rivers and set within a more general framework shortly thereafter. Since then, they have been applied to many different systems in diverse areas of application from ecology, through engineering to economics. It is worth noting that the new term ‘data-driven’ has been coined for computer-based analysis that derives results based directly on data. When applied to dynamic systems, such ‘data-driven modelling’ can mean the same as ‘data-based modelling’. However, The methodological tools used in such data-driven modelling activities are quite different from those in DBM modelling and are mainly ‘black-box’ in nature: indeed, the ultimate black box approach, Artificial Neural Network (ANN) modelling figures strongly in such activities (see e.g. https://en.wikipedia.org/wiki/Artificial_neural_network).
ANN models include complex interactions between the artificial ‘neurons’ and, as far as I am aware, no one has successfully ‘looked inside’ such ANN models and interpreted these complex interconnections in a physically meaningful, mechanistic manner. They are judged mainly by how well they are able to carry out the tasks, such as pattern recognition and prediction, for which they were intended and work well, rather than how they describe mechanisms that have a physical interpretation, as in DBM modelling. As an aid to such mechanistic interpretation, most of the DBM modelling in this book is carried out using stochastic linear or nonlinear continuous-time transfer function models that are directly equivalent to the differential equation models used in most of science and engineering. Consequently their parameters, which normally have a defined physical meaning, are important and these are estimated using the appropriate optimal estimation tools in the CAPTAIN Toolbox (e.g. in the case of linear models: RIVCBJID, RIVCBJ, SRIVCARMA, RIVCBJDD and RIVCBJFD). These yield ‘hybrid’ continuous-time models where the noise process associated with the stochastic model is in the form of a discrete-time AutoRegressive-Moving Average (ARMA) model, thus avoiding the problems and complexity associated with full stochastic differential equation modelling.
The book is predominantly a tutorial text, explaining in considerable detail how the CAPTAIN tools are utilised for the statistical identification of the model structure and the estimation of the parameters that characterise this structure. This is carried out by demonstrating how the DBM modelling can be applied successfully to the modelling of dynamic systems that have current global significance: global warming; the COVID-19 pandemic; and unemployment in the World’s largest economy, the United States of America. In the latter case, for example, it illustrates how the rise of right-wing neoliberal economic policies and, ultimately, the election of Donald Trump lead to the break-down of the model that quite successfully describes how the changes of public and private investment have affected unemployment from 1985 to 2015. For further information, see the Preface to the book in the link below. See also my other website https://wp.lancs.ac.uk/dbmmodeling/ which is concerned mainly with DBM modelling
