Scientific machine learning for inferring missing components of partially known mechanistic models, with biomedical applications

Modelling complex dynamics mechanistically can be challenging as gaps in the existing knowledge and/or difficulties obtaining certain parameter values often result in incomplete models. In such scenarios, recent advances in machine learning have demonstrated the possibility of developing partially-learned (or "grey box") models, wherein certain components of a mathematical (or "white box") model are set to be governed by a learned (or "black box") system. In our work, we replace unknown components of incomplete mathematical models with a neural network and use the available data to train the network to capture the missing dynamics of the system. This allows for a subsequent inference step, where the trained neural network embedded in the system equations is regressed down to mathematical expressions using symbolic regression. In this talk, we showcase three separate applications of this method. Firstly, we demonstrate that it is possible to learn governing equations of unobserved states in dynamical systems. Secondly, we present an alternative means of modelling ventricular interaction in a lumped parameter model of the cardiovascular system using this approach. Lastly, we show that improvements can be made to a slightly dated but widely used blood gas model.