I built symbolic-regression-biology, a Jupyter Notebook project on my GitHub, to benchmark symbolic regression on ground-truth biological dynamical systems defined in SBML. I want to find when these methods can recover biological-network governing equations and when they fail, evaluating outcomes through dynamical validation rather than symbolic similarity alone. The project started in 2026-01 and was last updated in 2026-03. It is listed on my github profile.
- My pipeline starts with curated SBML-based biological ODE models, simulates time-series data with numerical ODE solvers, adds biologically realistic noise, estimates time derivatives from observed trajectories, applies symbolic regression to rediscover governing equations, and compares recovered models with ground truth at the dynamical level.
I use the repressilator as an example benchmark: it is a gene regulatory network with nonlinear Hill-type repression dynamics, strong nonlinearity, oscillatory behavior, and identifiability issues under limited observations. Symbolic regression recovered low-complexity equations that fit observed derivatives well, but did not recover the original Hill-type repression terms. Simpler polynomial interaction terms approximated nonlinear biological rate laws, reflecting limitations of the symbolic operator set.
Despite the symbolic mismatch, the recovered system reproduced the true model’s steady-state behavior and preserved long-term stability, with minor discrepancies during early transient dynamics. This shows that dynamical equivalence can occur even when mechanistic identifiability fails. I consider dynamical validation essential for biological relevance; symbolic similarity alone is not enough to evaluate a recovered model.
- The failures motivate me to incorporate biological priors and structural constraints, including known interaction graphs and sparsity, and to optimize for dynamical behavior rather than symbolic exactness. This direction is motivated by hybrid approaches such as CellBox, which combine mechanistic modeling with machine learning to improve interpretability and robustness.
- My proposed next steps are to expand the operator set to better capture Hill-type kinetics, study partial observability and hidden variables, introduce biological priors into symbolic regression, and compare with hybrid neural–mechanistic models. Open questions include when symbolic regression can recover biological governing equations, how nonlinear kinetics and correlated variables impede mechanism recovery, and whether biological constraints improve recovery and dynamical predictions.
The README has a Results heading but supplies no quantitative benchmark scores, parameter values, sample sizes, or detailed experimental setup. The reported findings are qualitative; the available project description does not establish how performance varies across models or experimental conditions.