System identification poses a significant bottleneck to characterizing and controlling complex systems. This challenge is greatest when both the system states and parameters are not directly accessible, leading to a dual-estimation problem. Current approaches to such problems are limited in their ability to scale with many-parameter systems, as often occurs in networks. In the current work, we present a new, computationally efficient approach to treat large dual-estimation problems. In this work, we derive analytic back-propagated gradients for the Prediction Error Method which enables efficient and accurate identification of large systems. The PEM approach consists of directly integrating state estimation into a dual-optimization objective, leaving a differentiable cost/error function only in terms of the unknown system parameters, which we solve using numerical gradient/Hessian methods. Intuitively, this approach consists of solving for the parameters that generate the most accurate state estimator (Extended/Cubature Kalman Filter). We demonstrate that this approach is at least as accurate in state and parameter estimation as joint Kalman Filters (Extended/Unscented/Cubature) and Expectation-Maximization, despite lower complexity. We demonstrate the utility of our approach by inverting anatomically-detailed individualized brain models from human magnetoencephalography (MEG) data.