# Amortized Equation Discovery in Hybrid Dynamical Systems

arXiv: https://arxiv.org/abs/2406.03818 · HTML: https://mlsanity.com/paper/2406.03818/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Builds on (most cited first, 9 of 9)

- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [TimeGPT-1](https://mlsanity.com/paper/2310.03589/) (2023)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Collapsed Amortized Variational Inference for Switching Nonlinear Dynamical Systems](https://mlsanity.com/paper/1910.09588/) (2019)
- [Deep Explicit Duration Switching Models for Time Series](https://mlsanity.com/paper/2110.13878/) (2021)
- [Graph Switching Dynamical Systems](https://mlsanity.com/paper/2306.00370/) (2023)

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

- [Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis](https://mlsanity.com/paper/2406.08627/) (2024)
- [MultiEcho: An Experimental Science of Learned Worlds](https://mlsanity.com/paper/2609.33347/) (2026)

## Abstract (arXiv)

Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states. To learn the laws of systems, all previous methods for equation discovery in hybrid systems follow a two-stage paradigm, i.e. they first group time series into small cluster fragments and then discover equations in each fragment separately through methods in non-hybrid systems. Although effective, these methods do not fully take advantage of the commonalities in the shared dynamics of multiple fragments that are driven by the same equations. Besides, the two-stage paradigm breaks the interdependence between categorizing and representing dynamics that jointly form hybrid systems. In this paper, we reformulate the problem and propose an end-to-end learning framework, i.e. Amortized Equation Discovery (AMORE), to jointly categorize modes and discover equations characterizing the dynamics of each mode by all segments of the mode. Experiments on four hybrid and six non-hybrid systems show that our method outperforms previous methods on equation discovery, segmentation, and forecasting.