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Modeling an unknown dynamical system is crucial in order to predict thefuture behavior of the system. A standard approach is training recurrent modelson measurement data. While these models typically provide exact short-termpredictions, accumulating errors yield deteriorated long-term behavior. Incontrast, models with reliable long-term predictions can often be obtained,either by training a robust but less detailed model, or by leveragingphysics-based simulations. In both cases, inaccuracies in the models yield alack of short-time details. Thus, different models with contrastive propertieson different time horizons are available. This observation immediately raisesthe question: Can we obtain predictions that combine the best of both worlds?Inspired by sensor fusion tasks, we interpret the problem in the frequencydomain and leverage classical methods from signal processing, in particularcomplementary filters. This filtering technique combines two signals byapplying a high-pass filter to one signal, and low-pass filtering the other.Essentially, the high-pass filter extracts high-frequencies, whereas thelow-pass filter extracts low frequencies. Applying this concept to dynamicsmodel learning enables the construction of models that yield accurate long- andshort-term predictions. Here, we propose two methods, one being purelylearning-based and the other one being a hybrid model that requires anadditional physics-based simulator.

Combining Slow and Fast: Complementary Filtering for Dynamics Learning