# Neural Hybrid Automata: Learning Dynamics with Multiple Modes and Stochastic Transitions

arXiv: https://arxiv.org/abs/2106.04165 · HTML: https://mlsanity.com/paper/2106.04165/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Control](https://mlsanity.com/paper/2007.01926/) (2020)
- [Neural Ordinary Differential Equations for Intervention Modeling](https://mlsanity.com/paper/2010.08304/) (2020)
- [Learning Contact Dynamics using Physically Structured Neural Networks](https://mlsanity.com/paper/2102.11206/) (2021)
- [First Steps: Latent-Space Control with Semantic Constraints for Quadruped Locomotion](https://mlsanity.com/paper/2007.01520/) (2020)
- [A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems](https://mlsanity.com/paper/1502.01538/) (2015)

## Built on by (most cited first, 7 of 7)

- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Multi-Abstractive Neural Controller: An Efficient Hierarchical Control Architecture for Interactive Driving](https://mlsanity.com/paper/2305.14797/) (2023)
- [A Transition System Abstraction Framework for Neural Network Dynamical System Models](https://mlsanity.com/paper/2402.11739/) (2024)
- [Physics-Embedded Neural ODEs for Sim2Real Edge Digital Twins of Hybrid Power Electronics Systems](https://mlsanity.com/paper/2508.02887/) (2025)
- [SAC-MoE: Reinforcement Learning with Mixture-of-Experts for Control of Hybrid Dynamical Systems with Uncertainty](https://mlsanity.com/paper/2511.12361/) (2025)
- [Conservative Hybrid Graph Networks for Process Systems with Learned Routing](https://mlsanity.com/paper/2608.28896/) (2026)
- [Learning Continuous Neural Representation of Stochastic Hybrid Systems](https://mlsanity.com/paper/2609.38893/) (2026)

## Abstract (arXiv)

Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism for dynamical systems subject to discrete, possibly stochastic, state jumps and multi-modal continuous-time flows. Despite the versatility and importance of SHSs across applications, a general procedure for the explicit learning of both discrete events and multi-mode continuous dynamics remains an open problem. This work introduces Neural Hybrid Automata (NHAs), a recipe for learning SHS dynamics without a priori knowledge on the number of modes and inter-modal transition dynamics. NHAs provide a systematic inference method based on normalizing flows, neural differential equations and self-supervision. We showcase NHAs on several tasks, including mode recovery and flow learning in systems with stochastic transitions, and end-to-end learning of hierarchical robot controllers.