Learning PDE Time-Stepping with Neural Cellular Automata

arXiv:2608.30328 · cs.LG, stat.ML · Submitted 2026-08-31 · Read on arXiv

cs.LG, stat.ML

Submitted: 2026-08-31

Updated: 2026-08-31

Terminology

• Neural Cellular Automata — 13× in this paper
• Benchmark — 8× in this paper · explained in 2 episodes
• Adam — 7× in this paper · explained in 2 episodes
• Ablation — 6× in this paper · explained in 1 episode
• Accuracy — 5× in this paper · explained in 1 episode
• Robustness — 5× in this paper · explained in 5 episodes
• Fourier Neural Operator — 3× in this paper
• DeepONet — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Physical Constraints — 2× in this paper · explained in 7 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Ablation study — 1× in this paper · explained in 1 episode
• Computational Biology — 1× in this paper · explained in 2 episodes
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• PDE residual — 1× in this paper · explained in 2 episodes
• Physics-Informed Neural Network (PINN) — 1× in this paper · explained in 3 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes

Sources

• PinnDE: Physics-Informed Neural Networks for Solving Differential Equations
• Learning Coupled System Dynamics under Incomplete Physical Constraints and Missing Data

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