A New MIQCQP Approach to Symoblic Polynomial Regression:

Algorithmic searches for physical models have become increasingly popular in recent years, not least in chemical engineering where recent advances have supported the wider adoption of machine learning techniques. Existing parametric and non-parametric approaches such as sparse and symbolic regression often suffer from fundamental issues however, with overcomplexity and misspecification affecting the former and high computational complexity the latter. This paper presents a new mixed integer quadratically constrained quadratic programme (MIQCQP), which facilitates symbolic multivariate polynomial regression, seeking to strike a balance between these two methodologies. To this end, a new formulation is outlined and the effects of implementing a series of additional symmetry cuts, to help reduce computational times, are explored. The performance of this formulation is then assessed and compared against a tailored form of an existing symbolic regression formulation. Applications and possible expansions of the formulation are also briefly discussed laying the foundations for possible future work. Performance analysis revealed the new formulation to be effective at producing surrogate models to accurately describe non-linear behaviour, outperforming the tailored symbolic regression regarding both computational times and accuracy. The new formulation was also successfully applied to various chemical engineering examples surrounding non-linear dynamical systems and thermodynamic modelling, showing great potential for expansion and improvement. A major limitation of the formulation however, is its high degree of computational complexity, compared to alternative parametric techniques, currently limiting its application to smaller, less complex data sets.