Robust parameter estimation and identifiability analysis with hybrid neural ordinary differential equations in computational biology

Parameter estimation is one of the central challenges in computational biology. In this paper, we present an approach to estimate model parameters and assess their identifiability in cases where only partial knowledge of the system structure is available. The partially known model is embedded into a system of hybrid neural ordinary differential equations, with neural networks capturing unknown system components. Integrating neural networks into the model presents two main challenges: global exploration of the mechanistic parameter space during optimization and potential loss of parameter identifiability due to the neural network flexibility. To tackle these challenges, we treat biological parameters as hyperparameters, allowing for global search during hyperparameter tuning. We then conduct a posteriori identifiability analysis, extending a well-established method for mechanistic models. The pipeline performance is evaluated on three test cases designed to replicate real-world conditions, including noisy data and limited system observability.