# Learning Locally Interacting Discrete Dynamical Systems: Towards Data-Efficient and Scalable Prediction

arXiv: https://arxiv.org/abs/2404.06460 · HTML: https://mlsanity.com/paper/2404.06460/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 9 Apr 2024.

## Builds on (most cited first, 17 of 17)

- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Unsupervised Learning for Physical Interaction through Video Prediction](https://mlsanity.com/paper/1605.07157/) (2016)
- [SimVP: Simpler yet Better Video Prediction](https://mlsanity.com/paper/2206.05099/) (2022)
- [End-to-end Learning of Driving Models from Large-scale Video Datasets](https://mlsanity.com/paper/1612.01079/) (2016)
- [PredRNN++: Towards A Resolution of the Deep-in-Time Dilemma in Spatiotemporal Predictive Learning](https://mlsanity.com/paper/1804.06300/) (2018)
- [Multi-Agent Game Abstraction via Graph Attention Neural Network](https://mlsanity.com/paper/1911.10715/) (2019)
- [Social Learning in Multi Agent Multi Armed Bandits](https://mlsanity.com/paper/1910.02100/) (2019)
- [Cellular automata as convolutional neural networks](https://mlsanity.com/paper/1809.02942/) (2018)
- [Neural Dynamics on Complex Networks](https://mlsanity.com/paper/1908.06491/) (2019)
- [Learning Graph Cellular Automata](https://mlsanity.com/paper/2110.14237/) (2021)
- [Variational Neural Cellular Automata](https://mlsanity.com/paper/2201.12360/) (2022)
- [Attention-based Neural Cellular Automata](https://mlsanity.com/paper/2211.01233/) (2022)
- [DyNCA: Real-time Dynamic Texture Synthesis Using Neural Cellular Automata](https://mlsanity.com/paper/2211.11417/) (2022)
- [A Data-driven Understanding of COVID-19 Dynamics Using Sequential Genetic Algorithm Based Probabilistic Cellular Automata](https://mlsanity.com/paper/2008.12020/) (2020)
- [Forecasting Evolution of Clusters in Game Agents with Hebbian Learning](https://mlsanity.com/paper/2209.06904/) (2022)

## Built on by (most cited first, 5 of 5)

- [Learning Elementary Cellular Automata with Transformers](https://mlsanity.com/paper/2412.01417/) (2024)
- [Beyond Memorization: Extending Reasoning Depth with Recurrence, Memory and Test-Time Compute Scaling](https://mlsanity.com/paper/2508.16745/) (2025)
- [Online Relational Inference for Evolving Multi-agent Interacting Systems](https://mlsanity.com/paper/2411.01442/) (2024)
- [FLAMES: A Hybrid Spiking-State Space Model for Adaptive Memory Retention in Event-Based Learning](https://mlsanity.com/paper/2504.01257/) (2025)
- [AugRelNet: Relation-Augmented Dynamics for Structure Discovery and Forecasting from Limited Data](https://mlsanity.com/paper/2606.11251/) (2026)

## Abstract (arXiv)

Locally interacting dynamical systems, such as epidemic spread, rumor propagation through crowd, and forest fire, exhibit complex global dynamics originated from local, relatively simple, and often stochastic interactions between dynamic elements. Their temporal evolution is often driven by transitions between a finite number of discrete states. Despite significant advancements in predictive modeling through deep learning, such interactions among many elements have rarely explored as a specific domain for predictive modeling. We present Attentive Recurrent Neural Cellular Automata (AR-NCA), to effectively discover unknown local state transition rules by associating the temporal information between neighboring cells in a permutation-invariant manner. AR-NCA exhibits the superior generalizability across various system configurations (i.e., spatial distribution of states), data efficiency and robustness in extremely data-limited scenarios even in the presence of stochastic interactions, and scalability through spatial dimension-independent prediction.