Physics-encoded deep learning in identifying battery parameters without direct knowledge of ground truth

We show a method to embed physical laws and on-line observation into machine learning so that irrelevant low-cost battery data can be utilized to identify complex system parameters by machine learning without knowledge of their ground truth as the training data. Lithium diffusivity, a complicated function of lithium concentration, is a crucial parameter for battery performance but difficult to measure directly. We take diffusivity as an example and show that it can be obtained from easily measured sequence of battery voltage over time. In simulations, our results show that this method accurately quantifies not only the diffusivities of both positive and negative electrodes, but also as complex non-linear functions of lithium concentration, purely based on the cell voltage data requiring neither diffusivity nor concentration measurement. Notably, it can accurately predict nonmonotonic, many-to-one relations such as "w" shape functions. Moreover, this method is immune to measurement noise and capable of simultaneously estimating multiple parameters. In experiments, our method demonstrates more robust diffusivity estimation than a pure physics-based parameter fitting method and a widely used experimental technique. Our results suggest that the approach enables identifying physical parameters and their interdependence without direct measurements of those parameters.