Improving the Flexibility of Shape-Constrained Symbolic Regression with Extended Constraints

Abstract

We describe an approach to utilize a broader spectrum of domain knowledge to model magnetization curves for high magnetic field strengths 0 ≤ H≤ 10 6 with access to data points far below the saturation polarization. Thereby, we extend the implementation of Shape-Constrained Symbolic Regression. The extension allows the modification of model estimates by a given expression to apply additional sets of constraints. We apply the given expression of an Extended Constraint row-by-row and compare the minimum and maximum outputs with the target interval. Furthermore, we introduce regions and thresholds as additional tools for constraint description and soft constraint evaluation. Our achieved results demonstrate the positive impact of such additional knowledge. The logical downside is the dependence on that knowledge to describe applicable constraints. Nevertheless, the approach is a promising way to reduce the human calculation effort for extrapolating magnetization curves. For future work, we plan to combine soft and hard constraint evaluation as well as the utilization of structure template GP.