Physics Compliance as a Metric for Neural Network Uncertainty

Machine learning models are gradually gaining acceptance for deployment in science and engineering in recent years as industries mature and become more comfortable with data-driven methods, spanning the whole spectrum from data collection through to data engineering and data modelling. However, unease remains about the accuracy of predictions from these surrogate models when applied in industry, especially as these methods are often utilized as a black-box. Demand for uncertainty quantification has thus increased, especially in critical processes where one requires information about the degree of uncertainty in the prediction to better manage associated risks. Statistical methods such as Bayesian networks and deep ensembles have correspondingly been developed as possible solutions in recent years. While these methods are applicable across multiple domains, they can be computationally expensive or difficult to implement, and fail to capitalize on inherent physics present in many real-world problems. In this work, we thus propose to exploit our prior knowledge of the system, and use physics-based rules and relationships to estimate the degree of uncertainty in the model predictions. We compare the obtained results on a metasurface model system to state-of-the-art methods such as deep ensembles and hyperparameter ensembles. The promising results on this model system suggest that metrics to measure compliance to physics-based rules and relationships can indeed be a useful proxy for estimating these data-driven models' uncertainty, with these relations performing as well as conventional ensemble-based approaches.