Deep learning approach to parameter optimization for physiological models

The inference of nonlinear dynamics and parameters in biological data modeling is challenging. Conventional methodologies, based on hypothetical underlying mechanisms, complicate inference because standard parameter optimization methods are difficult to constrain to biological ranges. Here, we propose a novel method to evaluate and improve putative models using neural networks to simultaneously address biological modeling, parametrization, and parameter inference. As an example, utilizing data from clinical frequently sampled intravenous glucose tolerance testing, we introduce two physiological lipolysis models (with parameters) of the dynamics of glucose, insulin, and free fatty acids (FFA). Parameter values are obtained via optimization from the limited clinical data. We then generate large quantities of simulated data from the model by sampling parameters within physiological ranges. A convolutional neural network is trained to take the simulated data time courses of glucose, insulin, and FFA as input and output the model parameters. The performance of the trained neural network is evaluated for both parameter inference and reconstruction of trajectories over a testing dataset and from optimized model-fitting curves. We show that our methodology enables accurate parameter inference and trajectory reconstruction over the testing dataset and optimized model-fitting curves. The trained neural network produces consistently high $R^2$ values and low $p$ -values across different feature engineering strategies and training dataset sizes. We assess the impact of feature engineering choices and training dataset size on inference performance, demonstrating that appropriately designed feature transformations and certain activation function improve accuracy. Our results establish a deep learning framework for parameter inference in mathematical models, which can be adapted to various physiological systems.