Evaluating and Improving Symbolic Regression Methods for Biological Network Dynamics

This project aims to improve and evaluate symbolic regression methods for discovering interpretable mathematical models of biological network dynamics. A key challenge in this area is that, when working with real biological data, the true underlying equations are unknown, making it difficult to assess whether equation-discovery algorithms are accurate or biologically meaningful. To address this, I will generate synthetic time-series datasets from curated mechanistic models available in the BioModels database (e.g., SBML models), where the ground-truth equations are known. These datasets will be used to systematically evaluate and benchmark symbolic regression approaches, including PySR and neural-symbolic methods such as the Learning Law of Changes (LLC) framework. The project will also explore strategies to improve model identifiability and interpretability, including constrained search spaces and incorporation of biologically informed functional priors. The expected deliverables include: (1) a reproducible pipeline to generate simulation data from SBML models, (2) an evaluation framework to benchmark symbolic regression methods on equation recovery tasks, (3) implementation and comparison of PySR and LLC-based approaches, (4) strategies to address identifiability challenges in biological data, and (5) well-documented, open-source code integrated with existing SBML compatible tools.