Physics-Informed Neural Networks for Discovering Systems with Unmeasurable States with Application to Lithium-Ion Batteries

Combining machine learning with physics is a trending approach for discovering unknown dynamics, and one of such frameworks gaining attention is the physics-informed neural network (PINN). However, PINN often fails to optimize the network due to its difficulty in concurrently minimizing multiple losses originating from the system's governing equations. This problem can be more serious when the system's states are unmeasurable, as is the case for lithium-ion batteries. In this work, we introduce a robust method for training PINN that uses fewer loss terms and thus constructs a less complex landscape for optimization. In particular, instead of constructing losses from each differential equation, this method embeds the dynamics into a single loss function such that predicted states expanded in time given the dynamics are converted to a series of predicted outputs and compared with observed system outputs. Minimizing such a loss optimizes the network to predict states consistent with the physics. Further, system's unknown parameters are to be identified during training. For a demonstration, we apply it to a simple battery model to concurrently estimate its states and parameters.