Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions, accumulating errors yield deteriorated long-term behavior. In contrast, models with reliable long-term predictions can often be obtained, either by training a robust but less detailed model, or by leveraging physics-based simulations. In both cases, inaccuracies in the models yield a lack of short-time details. Thus, different models with contrastive properties on different time horizons are available. This observation immediately raises the question: Can we obtain predictions that combine the best of both worlds? Inspired by sensor fusion tasks, we interpret the problem in the frequency domain and leverage classical methods from signal processing, in particular complementary filters. This filtering technique combines two signals by applying a high-pass filter to one signal, and low-pass filtering the other. Essentially, the high-pass filter extracts high-frequencies, whereas the low-pass filter extracts low frequencies. Applying this concept to dynamics model learning enables the construction of models that yield accurate long- and short-term predictions. Here, we propose two methods, one being purely learning-based and the other one being a hybrid model that requires an additional physics-based simulator.

翻译：对未知动力学系统进行建模对于预测其未来行为至关重要。标准方法是基于测量数据训练循环模型。虽然这类模型通常能提供精确的短期预测，但累积误差会导致长期行为退化。相反，通过训练鲁棒但细节较少的模型，或利用基于物理的仿真，往往能获得具有可靠长期预测能力的模型。在这两种情况下，模型的精度不足都会导致缺乏短期细节。因此，我们获得了在不同时间尺度上具有对比属性的不同模型。这一观察立即引出一个问题：我们能否获得结合两者优势的预测结果？受传感器融合任务的启发，我们从频域角度解读该问题，并利用信号处理中的经典方法，尤其是互补滤波。这种滤波技术通过对一个信号应用高通滤波、对另一个信号应用低通滤波来融合两个信号。本质上，高通滤波提取高频成分，而低通滤波提取低频成分。将这一概念应用于动力学模型学习，能够构建出在长期和短期预测中均表现精准的模型。为此，我们提出了两种方法：一种是纯学习方法，另一种是需要额外物理仿真器的混合模型。