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Neural networks present a useful framework for learning complex dynamics, and are increasingly being considered as components to closed loop predictive control algorithms. However, if they are to be utilized in such safety-critical advisory settings, they must be provably "conformant" to the governing scientific (biological, chemical, physical) laws which underlie the modeled process. Unfortunately, this is not easily guaranteed as neural network models are prone to learn patterns which are artifacts of the conditions under which the training data is collected, which may not necessarily conform to underlying physiological laws. In this work, we utilize a formal range-propagation based approach for checking whether neural network models for predicting future blood glucose levels of individuals with type-1 diabetes are monotonic in terms of their insulin inputs. These networks are increasingly part of closed loop predictive control algorithms for "artificial pancreas" devices which automate control of insulin delivery for individuals with type-1 diabetes. Our approach considers a key property that blood glucose levels must be monotonically decreasing with increasing insulin inputs to the model. Multiple representative neural network models for blood glucose prediction are trained and tested on real patient data, and conformance is tested through our verification approach. We observe that standard approaches to training networks result in models which violate the core relationship between insulin inputs and glucose levels, despite having high prediction accuracy. We propose an approach that can learn conformant models without much loss in accuracy. 

In this paper, we provide an approach to data-driven control for artificial pancreas systems by learning neural network models of human insulin-glucose physiology from available patient data and using a mixed integer optimization approach to control blood glucose levels in real-time using the inferred models. First, our approach learns neural networks to predict the future blood glucose values from given data on insulin infusion and their resulting effects on blood glucose levels. However, to provide guarantees on the resulting model, we use quantile regression to fit multiple neural networks that predict upper and lower quantiles of the future blood glucose levels, in addition to the mean. Using the inferred set of neural networks, we formulate a model-predictive control scheme that adjusts both basal and bolus insulin delivery to ensure that the risk of harmful hypoglycemia and hyperglycemia are bounded using the quantile models while the mean prediction stays as close as possible to the desired target. We discuss how this scheme can handle disturbances from large unannounced meals as well as infeasibilities that result from situations where the uncertainties in future glucose predictions are too high. We experimentally evaluate this approach on data obtained from a set of 17 patients over a course of 40 nights per patient. Furthermore, we also test our approach using neural networks obtained from virtual patient models available through the UVA-Padova simulator for type-1 diabetes.