Combining Slow and Fast: Complementary Filtering for Dynamics Learning

TL;DR

This paper introduces a novel approach that combines fast and slow dynamics models using complementary filtering, inspired by sensor fusion, to improve long- and short-term predictions in dynamical systems.

Contribution

It proposes two methods, one purely learning-based and one hybrid with physics simulation, to integrate models with different temporal accuracies for better dynamics prediction.

Findings

Enhanced long-term prediction accuracy

Improved short-term detail preservation

Effective combination of models across time scales

Abstract

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.