Conformance verification for neural network models of glucose-insulin dynamics

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.