Physics Informed Machine Learning with Misspecified Priors: \\An analysis of Turning Operation in Lathe Machines

Zhiyuan Zhao, Xueying Ding, Gopaljee Atulya, Alex Davis, Aarti Singh

Keywords: Physics-Informed Learning

Abstract: The recent development of physics informed neural networks (PINNs) has explored the inclusion of prior physics knowledge into the objective function of deep learning models as differential equation loss component to supervise learning of complex systems under data-constrained settings. However, PINN framework requires that expert-provided knowledge about the physical system is perfectly accurate, neglecting cases where there is potential for fallibility in expert judgment. We extend this research to consider the effect of explicit fallible expert judgment in the learning process. First, we theoretically upper bound the effect of fallible expert-provided information on the convergence of PINNs to the true solution. We show how to opportunistically leverage fallible expert knowledge when data are scarce, and gracefully diminish reliance on inaccurate expert judgment as more data are acquired. Second, we examine the limitations of the PINN in learning noisy real-world physical systems, and apply a modified Seq2seq learning with applications in turning operation in lathe machines. We also propose a combination of PINN framework with recurrent neural networks for predicting system behavior outside the training domain.