# GEM: Group Enhanced Model for Learning Dynamical Control Systems

arXiv: https://arxiv.org/abs/2104.02844 · HTML: https://mlsanity.com/paper/2104.02844/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 54 references that are in the map.
- First posted on arXiv 7 Apr 2021.

## Builds on (most cited first, 29 of 29)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Learning Dexterous In-Hand Manipulation](https://mlsanity.com/paper/1808.00177/) (2018)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Sim-to-Real: Learning Agile Locomotion For Quadruped Robots](https://mlsanity.com/paper/1804.10332/) (2018)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Deep Dynamics Models for Learning Dexterous Manipulation](https://mlsanity.com/paper/1909.11652/) (2019)
- [B-Spline CNNs on Lie Groups](https://mlsanity.com/paper/1909.12057/) (2019)
- [A Game Theoretic Framework for Model Based Reinforcement Learning](https://mlsanity.com/paper/2004.07804/) (2020)
- [Neural Dynamic Policies for End-to-End Sensorimotor Learning](https://mlsanity.com/paper/2012.02788/) (2020)
- [SE3-Nets: Learning Rigid Body Motion using Deep Neural Networks](https://mlsanity.com/paper/1606.02378/) (2016)
- [Deep Learning on Lie Groups for Skeleton-based Action Recognition](https://mlsanity.com/paper/1612.05877/) (2016)
- [Model-based Reinforcement Learning: A Survey](https://mlsanity.com/paper/2006.16712/) (2020)
- [Learning Group Structure and Disentangled Representations of Dynamical Environments](https://mlsanity.com/paper/2002.06991/) (2020)
- [A Unified Bellman Equation for Causal Information and Value in Markov Decision Processes](https://mlsanity.com/paper/1703.01585/) (2017)
- [Bayesian deep learning with hierarchical prior: Predictions from limited and noisy data](https://mlsanity.com/paper/1907.04240/) (2019)
- [Models, Pixels, and Rewards: Evaluating Design Trade-offs in Visual Model-Based Reinforcement Learning](https://mlsanity.com/paper/2012.04603/) (2020)
- [SymmetryNet: Learning to Predict Reflectional and Rotational Symmetries of 3D Shapes from Single-View RGB-D Images](https://mlsanity.com/paper/2008.00485/) (2020)

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

- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures](https://mlsanity.com/paper/2505.19521/) (2025)

## Abstract (arXiv)

Learning the dynamics of a physical system wherein an autonomous agent operates is an important task. Often these systems present apparent geometric structures. For instance, the trajectories of a robotic manipulator can be broken down into a collection of its transitional and rotational motions, fully characterized by the corresponding Lie groups and Lie algebras. In this work, we take advantage of these structures to build effective dynamical models that are amenable to sample-based learning. We hypothesize that learning the dynamics on a Lie algebra vector space is more effective than learning a direct state transition model. To verify this hypothesis, we introduce the Group Enhanced Model (GEM). GEMs significantly outperform conventional transition models on tasks of long-term prediction, planning, and model-based reinforcement learning across a diverse suite of standard continuous-control environments, including Walker, Hopper, Reacher, Half-Cheetah, Inverted Pendulums, Ant, and Humanoid. Furthermore, plugging GEM into existing state of the art systems enhances their performance, which we demonstrate on the PETS system. This work sheds light on a connection between learning of dynamics and Lie group properties, which opens doors for new research directions and practical applications along this direction. Our code is publicly available at: https://tinyurl.com/GEMMBRL.