Please note: This PhD seminar will take place in DC 2314.
Lena Podina, PhD candidate
David R. Cheriton School of Computer Science
Supervisors: Professors Mohammad Kohandel, Ali Ghodsi
In engineering and applied mathematics, developing accurate mathematical models to predict and understand real-world phenomena is of utmost importance. Symbolic regression is a useful machine-learning based tool to fit models, but it can be computationally expensive. We present a new method for enhancing symbolic regression for differential equations via dimensional analysis, specifically the Buckingham $\pi$ theorem and Ipsen’s method. Since symbolic regression often suffers from high computational costs and overfitting, non-dimensionalizing datasets reduces the number of input variables, simplifies the search space, and ensures that derived equations are physically meaningful. As a first step, we combine dimensional analysis with the PySR symbolic regression algorithm to show that dimensional analysis significantly improves the accuracy of the recovered algebraic equation. The results demonstrate that transforming data into a dimensionless form decreases computation time and improves the training and test error of the recovered hidden term. Then, as our main contribution, we integrate dimensional analysis with Universal Physics-Informed Neural Networks, in order to recover hidden differential equation terms in a partial-knowledge scenario. These findings suggest that integrating dimensional analysis with symbolic regression could lower computational costs, enhance model interpretability, and increase accuracy, providing a robust framework for automated discovery of governing equations in complex systems when data is limited.