Use of physics-based models to interpret battery degradation data over the course of cycling can provide deeper physical insight into the internal states of the system and how they evolve. We present a neural network trained on simulations generated by a previously published physics-based model for a lithium trivanadate (LVO) cathode to estimate parameters that evolve over the course of cycling. We focus on the robustness of the neural network through two case studies that probe different kinds of discrepancies between model and experiment: nonideal data and imperfect model. In the former, the experimental protocols do not meet the assumption made in the training data generated by the physics-based model, while in the latter, the physics-based model fails to describe all of the measured cathode behavior even under ideal conditions. When there is total model-experiment agreement, a neural network estimates parameters with improved accuracy compared to a maximum likelihood analysis using the same set of simulations. However, in both types of model-experiment discrepancy, the neural network returned biased parameter estimates. We introduce a data augmentation procedure into the neural network training to mitigate these effects and improve robustness, and employ it to estimate parameters for a cycling LVO cathode.