Hybrid Neural Differential Equations to Model Unknown Mechanisms and States in Biology

Efforts to model complex biological systems increasingly face challenges from ambiguous relationships within the model, such as through partially unknown mechanisms or unmodelled intermediate states. Hybrid neural differential equations are a recent modeling framework which has been previously shown to enable identification and prediction of complex phenomena, especially in the context of partially unknown mechanisms. We extend the application of hybrid neural differential equations to enable incorporation of theorized but unmodelled states within differential equation models. We find that beyond their capability to incorporate partially unknown mechanisms, hybrid neural differential equations provide an effective method to include knowledge of unmeasured states into differential equation models.