# Combining Slow and Fast: Complementary Filtering for Dynamics Learning

arXiv: https://arxiv.org/abs/2302.13754 · HTML: https://mlsanity.com/paper/2302.13754/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 27 Feb 2023.

## Builds on (most cited first, 11 of 11)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [Feedforward Sequential Memory Networks: A New Structure to Learn Long-term Dependency](https://mlsanity.com/paper/1512.08301/) (2015)
- [The Statistical Recurrent Unit](https://mlsanity.com/paper/1703.00381/) (2017)
- [Cascaded Complementary Filter Architecture for Sensor Fusion in Attitude Estimation](https://mlsanity.com/paper/2107.03970/) (2021)
- [The Wheelbot: A Jumping Reaction Wheel Unicycle](https://mlsanity.com/paper/2207.06988/) (2022)
- [Low-pass Recurrent Neural Networks - A memory architecture for longer-term correlation discovery](https://mlsanity.com/paper/1805.04955/) (2018)

## Built on by (most cited first, 2 of 2)

- [Hybrid Modeling Design Patterns](https://mlsanity.com/paper/2401.00033/) (2023)
- [Learning Hybrid Dynamics Models With Simulator-Informed Latent States](https://mlsanity.com/paper/2309.02873/) (2023)

## Abstract (arXiv)

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.