Fig. 2: Results of inferring one-dimensional homogeneous network dynamics.
From: Learning interpretable network dynamics via universal neural symbolic regression
a Comparison of the accuracy on predictions (adjusted R2 score) and discovered equations (Recall) for reconstructing dynamics from six scenarios, including Biochemical (Bio), Gene regulatory (Gene), Mutualistic Interaction (MI), Lotka-Volterra (LV), Neural (Neur), and Epidemic (Epi) dynamics. TPSINDy’s results are highly dominated by its choice of function terms while our LLC significantly outperforms the comparative methods across all network dynamics scenarios. b Comparison of the average execution time across all dynamics for various methods. Note that the TPSINDy requires strong priors, i.e., decomposability of self and interaction dynamics, as well as pre-defined orthogonal elementary function terms. In contrast, others are based on the same level of assumption that only requires decomposability. By combining with transformer-based pre-trained symbolic regression in our pipeline, we achieve a good balance between efficiency and accuracy. c The NED (Normalized Estimation Error) between the predictive results produced by the discovered governing equations and ground truth in the LV scenario. d Comparison of the fitting coefficients in governing equations discovered by various methods. e Comparison of state prediction curves for an individual node.
