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

Beomseok Kang, Harshit Kumar, Minah Lee, Biswadeep Chakraborty, Saibal Mukhopadhyay

TL;DR

AR-NCA addresses predicting evolution in locally interacting discrete dynamical systems by learning unknown local transition rules with a memory-enabled, permutation-invariant neural cellular automaton. It combines a per-cell memory (LSTM) with cellular self-attention to efficiently propagate neighbor dynamics into each cell, yielding data-efficient and scalable predictions. Empirical results on forest fire, host-pathogen, and stock-market-like models show AR-NCA outperforms video-prediction networks and other NCAs, especially under limited data and large spatial scales. The approach offers a practical framework for data-efficient modeling of complex spatiotemporal systems driven by local interactions, with potential extensions to richer state spaces and continuous dynamics.

Abstract

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.

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

TL;DR

AR-NCA addresses predicting evolution in locally interacting discrete dynamical systems by learning unknown local transition rules with a memory-enabled, permutation-invariant neural cellular automaton. It combines a per-cell memory (LSTM) with cellular self-attention to efficiently propagate neighbor dynamics into each cell, yielding data-efficient and scalable predictions. Empirical results on forest fire, host-pathogen, and stock-market-like models show AR-NCA outperforms video-prediction networks and other NCAs, especially under limited data and large spatial scales. The approach offers a practical framework for data-efficient modeling of complex spatiotemporal systems driven by local interactions, with potential extensions to richer state spaces and continuous dynamics.

Abstract

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.
Paper Structure (22 sections, 6 equations, 6 figures, 5 tables)

This paper contains 22 sections, 6 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Background and Dataset
  3. System Formulation
  4. Problem Statement
  5. Dataset
  6. Forest Fire model
  7. Host-Pathogen model
  8. Stock Market model
  9. Related Work on Learning Dynamical Systems
  10. Neural Cellular Automata
  11. Proposed Approach
  12. Lack of memory function in existing NCAs
  13. Spatial dependency in CNN-based NCAs
  14. Attentive Recurrent Neural Cellular Automata
  15. Empirical Result
  16. ...and 7 more sections

Figures (6)

  • Figure 1: Synthetic discrete dynamical systems (a) forest fire model, (b) host-pathogen model, (c) stock market model. Their states are represented by distinct colors.
  • Figure 2: Spatial dependency on cell location in (a) convolution (Conv) and (b) self-attention (SA).
  • Figure 3: The overview of Attentive Recurrent Neural Cellular Automata architecture.
  • Figure 4: Comparison of data efficiency with video prediction networks in stochastic (a) forest fire, (b) host-pathogen, and (c) stock market models. The bar and line indicate the mean and standard deviation.
  • Figure 5: Comparison of data efficiency with other NCA networks. The NCA networks are trained and evaluated in the (a) deterministic dense forest with the different amount of training data. Similarly, stochastic (b) host-pathogen and (c) stock market models.
  • ...and 1 more figures